ENA, Section 1.4, Mentioned, A

Time bar (total: 8.5s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze4.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.6%50.4%0%0%0%0
0%0%49.6%50.4%0%0%0%1
0%0%49.6%50.4%0%0%0%2
50%24.8%24.8%50.4%0%0%0%3
75%37.2%12.4%50.4%0%0%0%4
87.5%43.4%6.2%50.4%0%0%0%5
93.8%46.5%3.1%50.4%0%0%0%6
96.9%48.1%1.6%50.4%0%0%0%7
98.4%48.8%0.8%50.4%0%0%0%8
99.2%49.2%0.4%50.4%0%0%0%9
99.6%49.4%0.2%50.4%0%0%0%10
99.8%49.5%0.1%50.4%0%0%0%11
99.9%49.6%0%50.4%0%0%0%12
Compiler

Compiled 12 to 10 computations (16.7% saved)

sample3.1s (35.9%)

Memory
28.4MiB live, 2 809.5MiB allocated
Samples
2.2s5 690×2valid
321.0ms2 470×1valid
7.0ms96×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.2s
ival-cos: 1.3s (57.1% of total)
ival-sub: 368.0ms (16.7% of total)
const: 270.0ms (12.3% of total)
adjust: 214.0ms (9.7% of total)
ival-<=: 73.0ms (3.3% of total)
ival-and: 12.0ms (0.5% of total)
exact: 5.0ms (0.2% of total)
ival-assert: 4.0ms (0.2% of total)
Bogosity

explain227.0ms (2.7%)

Memory
-3.1MiB live, 318.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
124132(7.236524015109223e-184)4(-2.723967465340699e-161)(-.f64 #s(literal 1 binary64) (cos.f64 x))
00-0-#s(literal 1 binary64)
00-0-(cos.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 #s(literal 1 binary64) (cos.f64 x))cancellation2520
Confusion
Predicted +Predicted -
+1204
-1320
Precision
0.47619047619047616
Recall
0.967741935483871
Confusion?
Predicted +Predicted MaybePredicted -
+12004
-13200
Precision?
0.47619047619047616
Recall?
0.967741935483871
Freqs
test
numberfreq
04
1252
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
138.0ms360×2valid
13.0ms146×1valid
0.0ms0valid
Compiler

Compiled 40 to 25 computations (37.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 129.0ms
adjust: 56.0ms (43.5% of total)
ival-cos: 56.0ms (43.5% of total)
ival-sub: 15.0ms (11.6% of total)
ival-true: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess27.0ms (0.3%)

Memory
-20.5MiB live, 17.3MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1168
2358
3558
4878
51018
61078
044
064
1104
2144
3194
4254
5334
6434
7544
8574
0574
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Outputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Symmetry

(abs x)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Compiler

Compiled 4 to 4 computations (0% saved)

simplify4.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
068
1108
2148
3198
4258
5338
6438
7548
8578
0578
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
Outputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x

localize105.0ms (1.2%)

Memory
-3.1MiB live, 114.8MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(cos.f64 x)
accuracy28.15918852535065
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Samples
87.0ms180×2valid
6.0ms73×1valid
0.0ms0valid
Compiler

Compiled 18 to 10 computations (44.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 84.0ms
ival-cos: 74.0ms (88.2% of total)
adjust: 5.0ms (6% of total)
ival-sub: 4.0ms (4.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Counts
2 → 10
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
Outputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(cos x)
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((- 1 (cos x)) (cos x))
0.0ms
x
@-inf
((- 1 (cos x)) (cos x))
0.0ms
x
@inf
((- 1 (cos x)) (cos x))

simplify508.0ms (6%)

Memory
26.0MiB live, 216.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041102
1101102
2246102
3588102
41237102
51916102
62187102
72836102
84071102
95644102
106541102
116820102
126859102
136859102
147273102
157549102
167590102
177592102
187592102
197592102
207592102
217602102
227602102
237602102
0850790
Stop Event
iter limit
node limit
Counts
10 → 10
Calls
Call 1
Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(cos x)
Outputs
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (*.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)

rewrite253.0ms (3%)

Memory
-54.3MiB live, 182.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046
066
1236
21426
311536
092406
Stop Event
iter limit
node limit
iter limit
Counts
2 → 314
Calls
Call 1
Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
Outputs
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (sin.f64 x) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (sin.f64 x) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (sin.f64 x) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (sin.f64 x) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) #s(literal -1 binary64))))
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(fma.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))) (/.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))))) (/.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))))))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cos.f64 x))))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))

eval31.0ms (0.4%)

Memory
41.7MiB live, 75.1MiB allocated
Compiler

Compiled 9 493 to 919 computations (90.3% saved)

prune11.0ms (0.1%)

Memory
-35.5MiB live, 15.9MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3204324
Fresh000
Picked101
Done000
Total3214325
Accuracy
100.0%
Counts
325 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
55.2%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
100.0%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
99.5%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify9.0ms (0.1%)

Memory
15.6MiB live, 15.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
cost-diff0
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
cost-diff0
#s(approx (cos x) #s(literal 1 binary64))
cost-diff0
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff0
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff0
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
cost-diff0
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019108
029108
151108
279108
3116108
4143108
5166108
6188108
7211108
8216108
0216108
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
x
Outputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
x

localize129.0ms (1.5%)

Memory
13.6MiB live, 206.1MiB allocated
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
accuracy0
(*.f64 x x)
accuracy0
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
accuracy28.15918852535065
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
accuracy0.3455941890115946
#s(approx (cos x) #s(literal 1 binary64))
accuracy28.15918852535065
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy0
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy0
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
accuracy0
(*.f64 x x)
accuracy0
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
accuracy0
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
accuracy0
(*.f64 x x)
accuracy0.29533016658331523
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
Samples
97.0ms180×2valid
15.0ms73×1valid
0.0ms0valid
Compiler

Compiled 187 to 37 computations (80.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 90.0ms
ival-cos: 41.0ms (45.7% of total)
ival-sub: 18.0ms (20.1% of total)
ival-mult: 12.0ms (13.4% of total)
adjust: 11.0ms (12.3% of total)
const: 4.0ms (4.5% of total)
ival-add: 2.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory
-21.8MiB live, 13.6MiB allocated
Counts
12 → 24
Calls
Call 1
Inputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
Outputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@inf
((- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1))
1.0ms
x
@-inf
((- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1))
1.0ms
x
@0
((- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1))

simplify127.0ms (1.5%)

Memory
25.7MiB live, 220.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061188
1150188
2380188
31013188
42531188
54932188
08204169
Stop Event
iter limit
node limit
Counts
24 → 24
Calls
Call 1
Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
Outputs
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (*.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* -1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/24 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* -1/24 (pow x 2))
(*.f64 #s(literal -1/24 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(cos x)
(cos.f64 x)
(* -1/2 (pow x 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)

rewrite272.0ms (3.2%)

Memory
-25.2MiB live, 336.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01993
02993
111093
271793
3601493
0845493
Stop Event
iter limit
node limit
iter limit
Counts
12 → 444
Calls
Call 1
Inputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
Outputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) x))
(*.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) x)
(*.f64 (neg.f64 (*.f64 x x)) #s(literal -1/2 binary64))
(*.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) x)
(*.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 x))
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 x x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x (neg.f64 (*.f64 #s(literal -1/2 binary64) x)))
(*.f64 x (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) x) x))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(*.f64 (/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x) (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/331776 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x)) (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/191102976 binary64) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/331776 binary64) (pow.f64 x #s(literal 8 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x) (pow.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x)) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))))
(*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (*.f64 x x)))
(*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (/.f64 (*.f64 x x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)))))
(*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 x x)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 x (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
(pow.f64 (/.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (*.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (neg.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (*.f64 x x)) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 x x) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (*.f64 x x) (neg.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 x (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) x)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 x (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x))) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))))
(/.f64 (*.f64 x x) (pow.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal -1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (*.f64 x x))))
(fma.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) x (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) #s(literal -1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) x) (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))

eval91.0ms (1.1%)

Memory
13.6MiB live, 127.3MiB allocated
Compiler

Compiled 13 101 to 1 676 computations (87.2% saved)

prune40.0ms (0.5%)

Memory
-14.3MiB live, 30.5MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New4851486
Fresh000
Picked044
Done000
Total4855490
Accuracy
100.0%
Counts
490 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
55.2%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
4.1%
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
100.0%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
99.5%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
Compiler

Compiled 48 to 37 computations (22.9% saved)

simplify3.0ms (0%)

Memory
3.1MiB live, 3.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (cos x) #s(literal 1 binary64))
cost-diff0
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0511
0611
1911
0911
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)

localize12.0ms (0.1%)

Memory
24.6MiB live, 24.6MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy0.3455941890115946
#s(approx (cos x) #s(literal 1 binary64))
Samples
8.0ms256×0valid
Compiler

Compiled 20 to 11 computations (45% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-cos: 2.0ms (52.4% of total)
ival-add: 1.0ms (26.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Counts
2 → 10
Calls
Call 1
Inputs
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
Outputs
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (cos x))
(cos x)
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((+ (cos x) 1) (cos x))
0.0ms
x
@inf
((+ (cos x) 1) (cos x))
0.0ms
x
@-inf
((+ (cos x) 1) (cos x))

simplify222.0ms (2.6%)

Memory
-10.1MiB live, 102.9MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02586
15086
210186
322886
441386
557286
668186
791586
8145786
9234086
10394786
11471886
12487986
13492086
14555086
15581486
16581486
17582286
18582286
19582286
20582286
21582486
0582474
Stop Event
iter limit
saturated
Counts
10 → 10
Calls
Call 1
Inputs
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (cos x))
(cos x)
Outputs
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)

rewrite308.0ms (3.6%)

Memory
-4.9MiB live, 164.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0510
0610
12210
212010
397710
0871610
Stop Event
iter limit
node limit
iter limit
Counts
2 → 272
Calls
Call 1
Inputs
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
Outputs
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64))) (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 9 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)))) #s(literal -1 binary64)))
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(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 9 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)))
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(*.f64 (pow.f64 (/.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))
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(*.f64 (/.f64 (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)))) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64))))
(*.f64 (*.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 9 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(*.f64 (-.f64 (*.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 6 binary64)) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -3 binary64))) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)) (/.f64 (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(*.f64 (fma.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(*.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
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(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)))
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(*.f64 (fma.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64))))
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(+.f64 (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64))))
(+.f64 (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64))) (*.f64 (pow.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
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(+.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64))) (*.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64)))))
(+.f64 (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(+.f64 (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (cos x) #s(literal 1 binary64)))))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64)))))
(+.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
(pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 #s(approx (cos x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 #s(approx (cos x) #s(literal 1 binary64))))

eval68.0ms (0.8%)

Memory
0.6MiB live, 54.0MiB allocated
Compiler

Compiled 10 754 to 602 computations (94.4% saved)

prune27.0ms (0.3%)

Memory
-24.2MiB live, 12.5MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New2801281
Fresh000
Picked101
Done044
Total2815286
Accuracy
100.0%
Counts
286 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
55.2%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
100.0%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
99.5%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
4.1%
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Compiler

Compiled 48 to 38 computations (20.8% saved)

simplify3.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Algorithm
egg-herbie
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
067
197
097
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(literal 2 binary64)

localize12.0ms (0.1%)

Memory
13.7MiB live, 13.7MiB allocated
Localize:

Found 1 expressions of interest:

NewMetricScoreProgram
accuracy0.3299692371757346
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Samples
8.0ms256×0valid
Compiler

Compiled 14 to 13 computations (7.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-cos: 2.0ms (52.5% of total)
ival-add: 1.0ms (26.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Counts
1 → 5
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Outputs
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (cos x))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
((+ (cos x) 1))
0.0ms
x
@inf
((+ (cos x) 1))
0.0ms
x
@-inf
((+ (cos x) 1))

simplify185.0ms (2.2%)

Memory
20.4MiB live, 57.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02244
14444
29544
321044
436544
549644
660544
782744
8136244
9217044
10345544
11393444
12401844
13405144
14467844
15494244
16494244
17494244
18494244
19494244
20494444
0494438
Stop Event
iter limit
saturated
Counts
5 → 5
Calls
Call 1
Inputs
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 1 (cos x))
Outputs
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 1 (cos x))
(+.f64 #s(literal 1 binary64) (cos.f64 x))

rewrite211.0ms (2.5%)

Memory
-13.3MiB live, 177.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
066
1226
21336
312056
084606
Stop Event
iter limit
node limit
saturated
Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))

eval1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Compiler

Compiled 63 to 23 computations (63.5% saved)

prune3.0ms (0%)

Memory
6.4MiB live, 6.4MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New505
Fresh000
Picked011
Done044
Total5510
Accuracy
100.0%
Counts
10 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.0%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
55.2%
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
100.0%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
99.5%
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
4.1%
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Compiler

Compiled 106 to 64 computations (39.6% saved)

regimes44.0ms (0.5%)

Memory
-15.3MiB live, 33.1MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Outputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
Calls

3 calls:

39.0ms
x
2.0ms
(cos.f64 x)
2.0ms
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 #s(literal 1 binary64) (cos.f64 x))
100.0%1(cos.f64 x)
Compiler

Compiled 7 to 7 computations (0% saved)

regimes7.0ms (0.1%)

Memory
14.2MiB live, 14.2MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
Outputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
Calls

3 calls:

2.0ms
x
2.0ms
(cos.f64 x)
2.0ms
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(-.f64 #s(literal 1 binary64) (cos.f64 x))
99.5%1(cos.f64 x)
Compiler

Compiled 7 to 7 computations (0% saved)

regimes24.0ms (0.3%)

Memory
-25.4MiB live, 12.5MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
Outputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
Calls

3 calls:

21.0ms
x
1.0ms
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
55.2%1x
55.2%1(-.f64 #s(literal 1 binary64) (cos.f64 x))
55.2%1(cos.f64 x)
Compiler

Compiled 7 to 7 computations (0% saved)

regimes4.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Calls

3 calls:

2.0ms
x
1.0ms
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
4.1%1(-.f64 #s(literal 1 binary64) (cos.f64 x))
4.1%1(cos.f64 x)
4.1%1x
Compiler

Compiled 7 to 7 computations (0% saved)

simplify24.0ms (0.3%)

Memory
25.0MiB live, 62.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01837
12637
23037
33237
43337
Stop Event
saturated
Calls
Call 1
Inputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
Outputs
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (+ (cos x) 1) #s(literal 2 binary64))

soundness2.4s (27.7%)

Memory
12.1MiB live, 480.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041102
1101102
2246102
3588102
41237102
51916102
62187102
72836102
84071102
95644102
106541102
116820102
126859102
136859102
147273102
157549102
167590102
177592102
187592102
197592102
207592102
217602102
227602102
237602102
0850790
02586
15086
210186
322886
441386
557286
668186
791586
8145786
9234086
10394786
11471886
12487986
13492086
14555086
15581486
16581486
17582286
18582286
19582286
20582286
21582486
0582474
01993
02993
111093
271793
3601493
0845493
Stop Event
done
iter limit
node limit
iter limit
iter limit
saturated
iter limit
node limit
Compiler

Compiled 65 to 43 computations (33.8% saved)

preprocess95.0ms (1.1%)

Memory
-21.8MiB live, 61.0MiB allocated
Remove

(abs x)

Compiler

Compiled 162 to 104 computations (35.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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