tanhf (example 3.4)

Time bar (total: 4.8s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze117.0ms (2.4%)

Memory
10.4MiB live, 156.0MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
37.5%37.5%62.5%0%0%0%0%4
43.8%43.7%56.2%0%0%0%0%5
46.9%46.9%53.1%0%0%0%0%6
48.4%48.4%51.5%0%0%0%0%7
49.2%49.2%50.8%0%0%0%0%8
49.6%49.6%50.4%0%0%0%0%9
49.8%49.8%50.2%0%0%0%0%10
49.9%49.9%50.1%0%0%0%0%11
50%49.9%50%0%0%0%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.9s (40.7%)

Memory
39.2MiB live, 1 677.7MiB allocated
Samples
684.0ms2 235×2valid
545.0ms4 208×0valid
187.0ms552×3valid
134.0ms1 258×1valid
4.0ms4valid
Precisions
Click to see histograms. Total time spent on operations: 1.3s
ival-cos: 826.0ms (62.7% of total)
ival-sin: 171.0ms (13% of total)
adjust: 115.0ms (8.7% of total)
ival-div: 102.0ms (7.7% of total)
ival-sub: 87.0ms (6.6% of total)
ival-true: 6.0ms (0.5% of total)
exact: 5.0ms (0.4% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain165.0ms (3.4%)

Memory
-15.2MiB live, 148.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
901(2.0453048744956706e+99)0-(-.f64 #s(literal 1 binary64) (cos.f64 x))
610-1(5.513025161591462e-158)(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
00-0-#s(literal 1 binary64)
00-0-(cos.f64 x)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 #s(literal 1 binary64) (cos.f64 x))cancellation913
/.f64(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))u/n600
(-.f64 #s(literal 1 binary64) (cos.f64 x))underflow60
Confusion
Predicted +Predicted -
+1502
-1103
Precision
0.9933774834437086
Recall
0.9868421052631579
Confusion?
Predicted +Predicted MaybePredicted -
+15020
-11102
Precision?
0.987012987012987
Recall?
1.0
Freqs
test
numberfreq
0105
1151
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
42.0ms148×2valid
26.0ms244×0valid
13.0ms34×3valid
10.0ms86×1valid
Compiler

Compiled 62 to 28 computations (54.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-cos: 40.0ms (54.6% of total)
ival-sin: 11.0ms (15% of total)
ival-sub: 8.0ms (10.9% of total)
adjust: 7.0ms (9.6% of total)
ival-div: 6.0ms (8.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess41.0ms (0.9%)

Memory
37.0MiB live, 37.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
13011
2738
31808
44438
56818
67068
067
0104
1204
2264
3374
4584
5814
61144
71884
83104
95194
105614
115644
125724
135784
145824
155894
165964
175974
05974
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
49.1%
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify28.0ms (0.6%)

Memory
-30.8MiB live, 6.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(cos.f64 x)
cost-diff0
(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff6592
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0617
01014
12014
22614
33714
45814
58114
611414
718814
831014
951914
1056114
1156414
1257214
1357814
1458214
1558914
1659614
1759714
059714
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize51.0ms (1.1%)

Memory
21.5MiB live, 21.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(sin.f64 x)
accuracy0
(cos.f64 x)
accuracy14.16355199414161
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy18.21478738576892
(-.f64 #s(literal 1 binary64) (cos.f64 x))
Samples
20.0ms74×2valid
13.0ms122×0valid
6.0ms17×3valid
5.0ms43×1valid
Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-cos: 21.0ms (60.3% of total)
ival-sin: 5.0ms (14.4% of total)
adjust: 4.0ms (11.5% of total)
ival-div: 3.0ms (8.6% of total)
ival-sub: 3.0ms (8.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated
Counts
4 → 20
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 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)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))
1.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))
1.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (cos x) (sin x))

simplify232.0ms (4.8%)

Memory
-5.2MiB live, 143.2MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079202
1224202
2555196
31661196
43000196
54247196
64597196
75328196
86820196
08376172
Stop Event
iter limit
node limit
Counts
20 → 19
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 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)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(cos x)
(sin x)
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* 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 (*.f64 x x) #s(literal 1/24 binary64) #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))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)

rewrite191.0ms (4%)

Memory
-16.8MiB live, 234.0MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0615
01012
13912
224512
3235511
0888511
Stop Event
iter limit
node limit
iter limit
Counts
4 → 615
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 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 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 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 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 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 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (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 (pow.f64 (*.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
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(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.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 (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 #s(literal -1 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (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))
(neg.f64 (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(cos.f64 x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (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) (neg.f64 (sin.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) (sin.f64 x))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))) (neg.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)))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64))) (neg.f64 (*.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))) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (*.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))) (sin.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (fma.f64 (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))) (pow.f64 (sin.f64 x) #s(literal -1 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 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64)) (*.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))) (neg.f64 (sin.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64)) (*.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))) (sin.f64 x)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (sin.f64 x)))
(sin.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 x))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sin.f64 x)))

eval140.0ms (2.9%)

Memory
10.1MiB live, 127.3MiB allocated
Compiler

Compiled 13 034 to 1 647 computations (87.4% saved)

prune33.0ms (0.7%)

Memory
-11.3MiB live, 27.8MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New6304634
Fresh000
Picked101
Done000
Total6314635
Accuracy
100.0%
Counts
635 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 34 to 29 computations (14.7% saved)

simplify26.0ms (0.5%)

Memory
37.2MiB live, 37.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
cost-diff6464
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01766
02458
14058
25558
37258
49658
512058
615358
722758
835058
955858
1060058
1160358
1261158
1361658
1462058
1562758
1666058
1768258
1868458
068458
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize98.0ms (2%)

Memory
-23.2MiB live, 96.7MiB allocated
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
accuracy0
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy0
(*.f64 x x)
accuracy0.03125
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy0.2752425248057415
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy29.062706835259927
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy29.068677087658386
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Samples
38.0ms74×2valid
28.0ms122×0valid
11.0ms17×3valid
9.0ms43×1valid
Compiler

Compiled 123 to 36 computations (70.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 61.0ms
ival-cos: 24.0ms (39.4% of total)
adjust: 8.0ms (13.1% of total)
ival-mult: 6.0ms (9.9% of total)
ival-tan: 5.0ms (8.2% of total)
ival-sin: 5.0ms (8.2% of total)
const: 4.0ms (6.6% of total)
ival-div: 3.0ms (4.9% of total)
ival-sub: 3.0ms (4.9% of total)
ival-pow: 2.0ms (3.3% of total)
ival-add: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
6.7MiB live, 6.7MiB allocated
Counts
8 → 13
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))
2.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (* 1/2 x)) (pow 1 -1/2))

simplify148.0ms (3.1%)

Memory
7.8MiB live, 82.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03998
111498
228598
366098
4122498
5280098
6363298
7448498
8490798
9545498
10607498
11683198
12740698
0814189
Stop Event
iter limit
node limit
Counts
13 → 13
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #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 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))

rewrite206.0ms (4.3%)

Memory
5.3MiB live, 152.1MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01754
02449
18349
245249
3393237
01156837
Stop Event
iter limit
node limit
iter limit
Counts
8 → 163
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
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(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal 1/576 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 #s(literal 1/24 binary64) x))) #s(literal 1/2 binary64))
(fma.f64 x (pow.f64 (*.f64 #s(literal 1/24 binary64) x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) #s(literal 1/24 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (/.f64 (*.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 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(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 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval34.0ms (0.7%)

Memory
-2.5MiB live, 33.2MiB allocated
Compiler

Compiled 4 771 to 746 computations (84.4% saved)

prune5.0ms (0.1%)

Memory
10.2MiB live, 10.2MiB allocated
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1862188
Fresh000
Picked134
Done000
Total1875192
Accuracy
100.0%
Counts
192 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
7.6%
#s(literal 1 binary64)
Compiler

Compiled 50 to 40 computations (20% saved)

simplify58.0ms (1.2%)

Memory
-41.4MiB live, 23.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 1/24 binary64) x)
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff320
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01341
01838
13636
25836
37336
49436
511836
615136
722536
834936
955536
1059736
1160036
1260836
1361436
1461836
1562536
1665836
1767636
1867836
067834
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
Outputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(*.f64 x x)
x
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize74.0ms (1.5%)

Memory
23.9MiB live, 95.9MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.04296875
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
accuracy0.29296875
(*.f64 #s(literal 1/24 binary64) x)
accuracy29.062706835259927
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
Samples
28.0ms74×2valid
19.0ms122×0valid
10.0ms17×3valid
7.0ms43×1valid
Compiler

Compiled 74 to 29 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-cos: 21.0ms (41.4% of total)
ival-sin: 7.0ms (13.8% of total)
adjust: 6.0ms (11.8% of total)
ival-mult: 6.0ms (11.8% of total)
ival-div: 3.0ms (5.9% of total)
ival-sub: 3.0ms (5.9% of total)
const: 3.0ms (5.9% of total)
ival-add: 1.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
8.8MiB live, 8.8MiB allocated
Counts
5 → 9
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(pow x 2)
(* 1/24 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
Calls

3 calls:

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

simplify163.0ms (3.4%)

Memory
6.3MiB live, 127.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03672
110672
225972
359572
499572
5171772
6304072
7420972
8516772
9585872
10674772
11717272
12795372
0807965
Stop Event
iter limit
node limit
Counts
9 → 9
Calls
Call 1
Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(pow x 2)
(* 1/24 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

rewrite162.0ms (3.4%)

Memory
-18.1MiB live, 174.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01337
01834
16832
247432
3483631
0878629
Stop Event
iter limit
node limit
iter limit
Counts
5 → 135
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(*.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal 1/4 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64)) (pow.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 3 binary64)))) (fma.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(*.f64 (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) x) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (pow.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))))
(*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(*.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))))
(*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (/.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(*.f64 x (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(fma.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/24 binary64)) (/.f64 (*.f64 #s(literal 1/24 binary64) x) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) x) x) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 #s(literal 1/576 binary64) (*.f64 x x)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 #s(literal 1/576 binary64) (*.f64 x x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (exp.f64 (log.f64 #s(literal 1/24 binary64))) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (*.f64 #s(literal 1/576 binary64) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) x) x) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) x) x) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/24 binary64)) #s(literal 1/24 binary64)) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) (/.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/24 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 (*.f64 #s(literal 1/24 binary64) x))) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(fma.f64 x (exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 1/24 binary64)))) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x (/.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/24 binary64)) #s(literal 1/24 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(fma.f64 x (*.f64 (*.f64 #s(literal 1/24 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (*.f64 x (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 x (/.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (neg.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(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 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) x)
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (neg.f64 x))) (exp.f64 (log.f64 #s(literal -2 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)))

eval20.0ms (0.4%)

Memory
2.0MiB live, 37.4MiB allocated
Compiler

Compiled 4 345 to 550 computations (87.3% saved)

prune5.0ms (0.1%)

Memory
12.9MiB live, 12.9MiB allocated
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New1430143
Fresh000
Picked022
Done033
Total1435148
Accuracy
100.0%
Counts
148 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
54.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
7.6%
#s(literal 1 binary64)
Compiler

Compiled 110 to 65 computations (40.9% saved)

regimes6.0ms (0.1%)

Memory
12.5MiB live, 12.5MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

3.0ms
x
3.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes14.0ms (0.3%)

Memory
-35.3MiB live, 10.6MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
#s(literal 1 binary64)
Calls

2 calls:

12.0ms
x
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
58.1%2x
57.9%2(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory
3.6MiB live, 3.6MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(literal 1 binary64)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
58.1%2x
Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory
4.4MiB live, 4.4MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(literal 1 binary64)
Calls

2 calls:

2.0ms
x
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
57.7%2(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
57.8%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
4.4MiB live, 4.4MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 1 binary64)
Outputs
#s(literal 1 binary64)
Calls

2 calls:

1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
7.6%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
7.6%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch26.0ms (0.5%)

Memory
12.3MiB live, 46.3MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
24.0ms
0.0002246022790819983
206.4795282411465
Samples
13.0ms144×0valid
Compiler

Compiled 181 to 163 computations (9.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-cos: 4.0ms (39.1% of total)
ival-sin: 4.0ms (39.1% of total)
ival-sub: 1.0ms (9.8% of total)
ival-div: 1.0ms (9.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
1.0ms
0.0002246022790819983
206.4795282411465
Compiler

Compiled 163 to 154 computations (5.5% saved)

bsearch1.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
1.0ms
0.0002246022790819983
206.4795282411465
Compiler

Compiled 118 to 127 computations (-7.6% saved)

simplify24.0ms (0.5%)

Memory
-3.3MiB live, 75.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02365
12965
Stop Event
saturated
Calls
Call 1
Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness680.0ms (14.2%)

Memory
-34.4MiB live, 309.6MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0615
01012
13912
224512
3235511
0888511
01754
02449
18349
245249
3393237
01156837
079202
1224202
2555196
31661196
43000196
54247196
64597196
75328196
86820196
08376172
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
Compiler

Compiled 155 to 96 computations (38.1% saved)

preprocess75.0ms (1.6%)

Memory
27.6MiB live, 105.1MiB allocated
Remove

(negabs x)

Compiler

Compiled 168 to 84 computations (50% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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