sintan (problem 3.4.5)

Time bar (total: 12.5s)

analyze516.0ms (4.1%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.9%50.1%0%0%0%0
0%0%49.9%50.1%0%0%0%1
0%0%49.9%50.1%0%0%0%2
0%0%49.9%50.1%0%0%0%3
0%0%49.9%50.1%0%0%0%4
0%0%49.9%50.1%0%0%0%5
0%0%49.9%50.1%0%0%0%6
0%0%49.9%50.1%0%0%0%7
0%0%49.9%50.1%0%0%0%8
0%0%49.9%50.1%0%0%0%9
0%0%49.9%50.1%0%0%0%10
0%0%49.9%50.1%0%0%0%11
0%0%49.9%50.1%0%0%0%12
Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 296.0ms
...c/correct-round.rkt:119:19: 122.0ms (41.2% of total)
ival-sub: 44.0ms (14.9% of total)
ival-<=: 42.0ms (14.2% of total)
ival-sin: 36.0ms (12.2% of total)
ival-tan: 30.0ms (10.1% of total)
ival-div: 15.0ms (5.1% of total)
ival-and: 5.0ms (1.7% of total)
backward-pass: 2.0ms (0.7% of total)

sample8.7s (70%)

Results
6.0s4112×2valid
1.5s1280×3valid
812.0ms2787×1valid
8.0ms77×0valid
Precisions
Click to see histograms. Total time spent on operations: 7.7s
ival-tan: 4.3s (55.4% of total)
ival-sin: 2.1s (27.6% of total)
backward-pass: 369.0ms (4.8% of total)
ival-sub: 334.0ms (4.3% of total)
...c/correct-round.rkt:119:19: 326.0ms (4.2% of total)
ival-div: 175.0ms (2.3% of total)
ival-<=: 90.0ms (1.2% of total)
ival-and: 11.0ms (0.1% of total)
Bogosity

preprocess109.0ms (0.9%)

Algorithm
egg-herbie
Rules
1280×sum5-define
800×sum4-define
676×fnmadd-define
610×fnmadd-define
594×sum3-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01332
13730
29027
327327
472427
5155527
6274927
7278727
8315627
9317227
069
1139
2239
3429
4819
51909
65139
711019
823659
925579
1025769
1125849
025849
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Call 2
Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(/ (- eps (sin eps)) (- eps (tan eps)))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
(/ (- eps (sin eps)) (- (tan eps) eps))
Symmetry

(abs eps)

explain923.0ms (7.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1620-3(7.654716029471653e-105)(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
970-0-(-.f64 eps (sin.f64 eps))
970-0-(-.f64 eps (tan.f64 eps))
00-0-(sin.f64 eps)
00-0-eps
00-0-(tan.f64 eps)
Results
546.0ms82×3valid
298.0ms238×2valid
41.0ms188×1valid
0.0ms0valid
Compiler

Compiled 58 to 20 computations (65.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 842.0ms
ival-tan: 660.0ms (78.4% of total)
ival-sin: 141.0ms (16.7% of total)
ival-sub: 17.0ms (2% of total)
backward-pass: 16.0ms (1.9% of total)
ival-div: 7.0ms (0.8% of total)
const: 1.0ms (0.1% of total)

eval0.0ms (0%)

Compiler

Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
0.9%
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Compiler

Compiled 10 to 6 computations (40% saved)

simplify84.0ms (0.7%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 eps (tan.f64 eps))
cost-diff0
(sin.f64 eps)
cost-diff0
(-.f64 eps (sin.f64 eps))
cost-diff0
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Rules
676×fnmadd-define
450×fmsub-define
440×fnmsub-define
394×fmm-def
368×fma-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0622
11322
22322
34222
48122
519022
651322
7110122
8236522
9255722
10257622
11258422
0258422
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
eps
(sin eps)
(- eps (tan eps))
(tan eps)
Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(- eps (sin eps))
(-.f64 eps (sin.f64 eps))
eps
(sin eps)
(sin.f64 eps)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize226.0ms (1.8%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sin.f64 eps)
accuracy66.0%
(-.f64 eps (sin.f64 eps))
accuracy66.0%
(-.f64 eps (tan.f64 eps))
accuracy37.9%
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Results
137.0ms119×2valid
53.0ms41×3valid
25.0ms94×1valid
0.0ms0valid
Compiler

Compiled 24 to 7 computations (70.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 182.0ms
ival-tan: 97.0ms (53.2% of total)
ival-sin: 65.0ms (35.6% of total)
backward-pass: 8.0ms (4.4% of total)
ival-sub: 8.0ms (4.4% of total)
ival-div: 4.0ms (2.2% of total)
const: 0.0ms (0% of total)

series4.0ms (0%)

Counts
4 → 48
Calls
Call 1
Inputs
#<alt (/ (- eps (sin eps)) (- eps (tan eps)))>
#<alt (- eps (sin eps))>
#<alt (sin eps)>
#<alt (- eps (tan eps))>
Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms
eps
@-inf
(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms
eps
@0
(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms
eps
@-inf
(- eps (tan eps))
0.0ms
eps
@inf
(- eps (tan eps))

rewrite348.0ms (2.8%)

Algorithm
batch-egg-rewrite
Rules
3748×*-lowering-*.f32
3748×*-lowering-*.f64
3480×/-lowering-/.f32
3480×/-lowering-/.f64
1496×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0619
14619
241919
3632119
0817719
Stop Event
iter limit
node limit
Counts
4 → 373
Calls
Call 1
Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
(sin eps)
(- eps (tan eps))
Outputs
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (sin.f64 eps) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))) (/.f64 (sin.f64 eps) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps eps)) (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps eps)))
(+.f64 (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (+.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (*.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (*.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (*.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (*.f64 (*.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (*.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (*.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (*.f64 (*.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (*.f64 (+.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (*.f64 (*.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (*.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (*.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (*.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (*.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (*.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (*.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 2 binary64))))) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 (*.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 (*.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
(-.f64 (/.f64 (*.f64 eps eps) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 2 binary64))))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (*.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 2 binary64)) (*.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 2 binary64)) (*.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps)))))))
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(*.f64 (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(*.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(*.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(*.f64 (+.f64 eps (tan.f64 eps)) (*.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))))
(*.f64 (+.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))) (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(*.f64 (/.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (pow.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (+.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (*.f64 eps eps)))))
(*.f64 (/.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (pow.f64 (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(*.f64 (/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (+.f64 (*.f64 eps eps) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps))))

simplify246.0ms (2%)

Algorithm
egg-herbie
Rules
4708×*-lowering-*.f32
4708×*-lowering-*.f64
1320×+-lowering-+.f64
1320×+-lowering-+.f32
1274×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0148547
1457499
21536461
36921461
08078461
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps #s(literal 27/112000 binary64)))))))) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(+.f64 (*.f64 (sin.f64 eps) (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (*.f64 (sin.f64 eps) (/.f64 (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (*.f64 eps eps))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 eps) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps)) #s(literal -1 binary64)))) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (*.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/120 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/5040 binary64)))))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -2/15 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(*.f64 eps (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/3 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -2/15 binary64) (*.f64 eps (*.f64 eps #s(literal -17/315 binary64)))))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -17/315 binary64) (*.f64 (*.f64 eps eps) #s(literal -62/2835 binary64)))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) eps) (cos.f64 eps))))

eval48.0ms (0.4%)

Compiler

Compiled 12278 to 1225 computations (90% saved)

prune99.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4183421
Fresh000
Picked101
Done000
Total4193422
Accuracy
100.0%
Counts
422 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
99.8%
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
99.4%
#s(literal -1/2 binary64)
Compiler

Compiled 24 to 18 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
cost-diff0
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
cost-diff0
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
cost-diff0
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
cost-diff0
(*.f64 eps eps)
cost-diff0
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
cost-diff0
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
Rules
140×fma-define
104×fma-lowering-fma.f32
104×fma-lowering-fma.f64
76×*-lowering-*.f32
76×*-lowering-*.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01269
13165
27465
314165
418265
518565
018565
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
-1/2
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
9/40
(* eps eps)
eps
-1/2
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
9/40
(* (* eps eps) -27/2800)
(* eps eps)
-27/2800
-1/2
Outputs
-1/2
#s(literal -1/2 binary64)
(+ (* 9/40 (* eps eps)) -1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(* 9/40 (* eps eps))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
9/40
#s(literal 9/40 binary64)
(* eps eps)
(*.f64 eps eps)
eps
-1/2
#s(literal -1/2 binary64)
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps #s(literal -27/2800 binary64))))))
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps #s(literal -27/2800 binary64)))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps #s(literal -27/2800 binary64)))))
(+ 9/40 (* (* eps eps) -27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps #s(literal -27/2800 binary64))))
9/40
#s(literal 9/40 binary64)
(* (* eps eps) -27/2800)
(*.f64 eps (*.f64 eps #s(literal -27/2800 binary64)))
(* eps eps)
(*.f64 eps eps)
-27/2800
#s(literal -27/2800 binary64)
-1/2
#s(literal -1/2 binary64)

localize69.0ms (0.6%)

Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
accuracy99.8%
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
accuracy99.7%
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
accuracy99.6%
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
accuracy100.0%
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
accuracy100.0%
(*.f64 eps eps)
accuracy99.8%
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
Results
37.0ms232×0valid
8.0ms3valid
3.0ms10×1valid
2.0ms2valid
Compiler

Compiled 73 to 13 computations (82.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
ival-mult: 13.0ms (42.4% of total)
...c/correct-round.rkt:119:19: 11.0ms (35.9% of total)
ival-add: 5.0ms (16.3% of total)
backward-pass: 1.0ms (3.3% of total)
const: 0.0ms (0% of total)

series6.0ms (0.1%)

Counts
8 → 96
Calls
Call 1
Inputs
#<alt (+ (* 9/40 (* eps eps)) -1/2)>
#<alt (* 9/40 (* eps eps))>
#<alt (* eps eps)>
#<alt (+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)>
#<alt (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))>
#<alt (* eps (+ 9/40 (* (* eps eps) -27/2800)))>
#<alt (+ 9/40 (* (* eps eps) -27/2800))>
#<alt (* (* eps eps) -27/2800)>
Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* 9/40 eps)>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
Calls

24 calls:

TimeVariablePointExpression
2.0ms
eps
@inf
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
1.0ms
eps
@0
(+ (* 9/40 (* eps eps)) -1/2)
0.0ms
eps
@inf
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
0.0ms
eps
@-inf
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
0.0ms
eps
@inf
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)

rewrite361.0ms (2.9%)

Algorithm
batch-egg-rewrite
Rules
3976×*-lowering-*.f32
3976×*-lowering-*.f64
2082×/-lowering-/.f32
2082×/-lowering-/.f64
1668×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01258
17254
256854
3631454
0815754
Stop Event
iter limit
node limit
Counts
8 → 276
Calls
Call 1
Inputs
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
(* eps eps)
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
(* (* eps eps) -27/2800)
Outputs
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(+.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64)))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 9/40 binary64) eps) eps #s(literal -1/2 binary64))
(neg.f64 (/.f64 (+.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))))))
(neg.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) #s(literal -1/4 binary64)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64)) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (neg.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64))))) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))))
(/.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) #s(literal -1/4 binary64)) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (neg.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64))))))
(/.f64 (+.f64 (neg.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64))))) #s(literal 1/4 binary64)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64)) #s(literal -1/2 binary64)))
(/.f64 (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))) (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))) (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) #s(literal -729/512000 binary64))))))
(/.f64 (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) #s(literal -1/64 binary64)) (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))) (+.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal 1/8 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) #s(literal -1/64 binary64)) (*.f64 (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal 81/6400 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64))) (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64))))) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -9/40 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal -1/16 binary64)) (*.f64 (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) #s(literal 1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal -1/512 binary64) (*.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) #s(literal -729/512000 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64))))))
(/.f64 (*.f64 (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64))))))
(/.f64 (*.f64 (+.f64 (*.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal 81/6400 binary64)))) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (+.f64 (*.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)))) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (neg.f64 (*.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))))))
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(/.f64 (*.f64 (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))) #s(literal -729/64000 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -81/1600 binary64) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))))) (neg.f64 (+.f64 #s(literal -9/40 binary64) (neg.f64 (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))))
(/.f64 (neg.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) #s(literal -81/1600 binary64))) (neg.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))) (+.f64 (*.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))) (*.f64 (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))) (*.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))))) (+.f64 (/.f64 #s(literal 81/1600 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (/.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 387420489/262144000000000 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64))) (*.f64 #s(literal 387420489/481890304000000000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))) (+.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64))) #s(literal 729/64000 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 531441/4096000000 binary64) (*.f64 #s(literal 387420489/481890304000000000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))) (+.f64 #s(literal 729/64000 binary64) (*.f64 #s(literal 19683/21952000000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))))))
(/.f64 (*.f64 (-.f64 #s(literal 531441/4096000000 binary64) (*.f64 #s(literal 387420489/481890304000000000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))) (+.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) (+.f64 #s(literal 81/1600 binary64) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64))))))))
(/.f64 (*.f64 (-.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) #s(literal 531441/61465600000000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))) (+.f64 #s(literal 81/1600 binary64) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))))))
(*.f64 (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))))
(*.f64 (+.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))) #s(literal -729/64000 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))))
(*.f64 (+.f64 #s(literal -81/1600 binary64) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -9/40 binary64) (neg.f64 (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64))))))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))))) (+.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/2800 binary64)))) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))))
(*.f64 (+.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)))) #s(literal -81/1600 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))
(*.f64 (/.f64 (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64)))) (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(*.f64 (/.f64 (+.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))) (+.f64 #s(literal 531441/4096000000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))))))) (+.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))) (-.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))) #s(literal 81/1600 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 729/64000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)))) (-.f64 #s(literal 6561/2560000 binary64) (*.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64))) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))) (-.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps eps))) #s(literal -729/7840000 binary64))) (+.f64 #s(literal 729/64000 binary64) (*.f64 #s(literal 19683/21952000000 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps eps))))))) (+.f64 #s(literal 81/1600 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)))))
(*.f64 eps (*.f64 eps #s(literal -27/2800 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(*.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps #s(literal -27/2800 binary64)) eps)

simplify167.0ms (1.3%)

Algorithm
egg-herbie
Rules
1992×fma-lowering-fma.f32
1992×fma-lowering-fma.f64
1658×*-lowering-*.f32
1658×*-lowering-*.f64
1460×fmm-def
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040614
1107590
2271590
3804579
42555579
56516579
08490579
Stop Event
iter limit
node limit
Counts
96 → 96
Calls
Call 1
Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* 9/40 eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 3))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 3))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(*.f64 eps (*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(*.f64 eps (*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(*.f64 #s(literal 9/40 binary64) (*.f64 eps eps))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* -27/2800 (pow eps 4))
(*.f64 eps (*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* -27/2800 (pow eps 4))
(*.f64 eps (*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(* 9/40 eps)
(*.f64 #s(literal 9/40 binary64) eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 3))
(*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 3))
(*.f64 #s(literal -27/2800 binary64) (*.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))

eval82.0ms (0.7%)

Compiler

Compiled 13071 to 1086 computations (91.7% saved)

prune34.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3900390
Fresh000
Picked033
Done000
Total3903393
Accuracy
100.0%
Counts
393 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
99.8%
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
99.4%
#s(literal -1/2 binary64)
Compiler

Compiled 55 to 35 computations (36.4% saved)

regimes5.0ms (0%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(literal -1/2 binary64)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Outputs
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
Calls

2 calls:

3.0ms
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
2.0ms
eps
Results
AccuracySegmentsBranch
100.0%1eps
100.0%1(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(literal -1/2 binary64)
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
Outputs
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
Calls

1 calls:

1.0ms
eps
Results
AccuracySegmentsBranch
99.8%1eps
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal -1/2 binary64)
Outputs
#s(literal -1/2 binary64)
Calls

1 calls:

1.0ms
eps
Results
AccuracySegmentsBranch
99.4%1eps
Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11921
Stop Event
saturated
Calls
Call 1
Inputs
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
Outputs
(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
#s(literal -1/2 binary64)

soundness371.0ms (3%)

Rules
4708×*-lowering-*.f32
4708×*-lowering-*.f64
1320×+-lowering-+.f64
1320×+-lowering-+.f32
1274×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0148547
1457499
21536461
36921461
08078461
Stop Event
done
iter limit
node limit
Compiler

Compiled 46 to 30 computations (34.8% saved)

preprocess35.0ms (0.3%)

Remove

(abs eps)

Compiler

Compiled 196 to 120 computations (38.8% saved)

end0.0ms (0%)

Profiling

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