Details

Time bar (total: 16.6s)

sample81.0ms

Algorithm
intervals
Results
40.0ms125×body160valid
19.0ms131×body80valid

simplify93.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
08236
131036
2105431
3485530
4500130

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.1b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.4b
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
13.8b
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
Counts
4 → 82
Calls
4 calls:
4.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
4.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
0.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

series258.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
11.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
79.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
157.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03351396
113571221
250011163

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
0.5b
(/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))
0.7b
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
13.8b
(fma (/ (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (fma 0.284496736 (/ 1 (fma 0.3275911 (fabs x) 1.0)) (/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))) (/ (* 1 1.061405429) (pow (fma 0.3275911 (fabs x) 1.0) 4)))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
32×add-exp-log
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×unpow-prod-down
20×associate-/r*
15×div-exp
11×add-cbrt-cube
7×pow-to-exp pow-exp sqr-pow
6×1-exp cube-prod prod-exp
5×pow1 unpow2
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv rec-exp pow-unpow
2×cube-mult frac-2neg unpow3 clear-num div-inv
1×pow-flip pow-pow cbrt-unprod fma-udef inv-pow
Counts
4 → 137
Calls
4 calls:
5.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
5.0ms
(/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))
11.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
0.0ms
(fma (/ (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (fma 0.284496736 (/ 1 (fma 0.3275911 (fabs x) 1.0)) (/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))) (/ (* 1 1.061405429) (pow (fma 0.3275911 (fabs x) 1.0) 4)))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

series218.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
24.0ms
(/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))
19.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
168.0ms
(fma (/ (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (fma 0.284496736 (/ 1 (fma 0.3275911 (fabs x) 1.0)) (/ (* 1 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 3))) (/ (* 1 1.061405429) (pow (fma 0.3275911 (fabs x) 1.0) 4)))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

simplify83.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05301528
128141206
250011194

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
0.5b
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3))
0.8b
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
13.8b
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
43×add-sqr-sqrt
41×add-cube-cbrt
36×times-frac
17×associate-+l+
15×unpow-prod-down prod-diff add-log-exp
12×cube-prod associate-/r*
10×add-exp-log
8×associate--l+
6×add-cbrt-cube
5×pow1 fma-def sqr-pow
4×expm1-log1p-u cube-mult diff-log unpow3 log1p-expm1-u
3×sub-neg pow-unpow fma-neg div-exp sum-log associate-/l*
2×pow-to-exp flip3-- frac-add pow-exp flip-- fma-udef distribute-lft-out distribute-lft-out--
1×cbrt-undiv +-commutative associate-+l- pow-pow frac-2neg flip3-+ clear-num flip-+ div-inv unpow2 difference-of-squares
Counts
4 → 150
Calls
4 calls:
5.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
5.0ms
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3))
3.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
86.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 2)
24.0ms
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3))
97.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
245.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

simplify113.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06704183
131933532
250013443

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
0.8b
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
13.8b
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))
13.8b
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
34×associate-+l+
30×prod-diff
28×add-sqr-sqrt
26×add-log-exp
24×add-cube-cbrt
16×associate--l+
10×fma-def
8×diff-log
6×sub-neg fma-neg sum-log
4×pow1 add-exp-log expm1-log1p-u flip3-- frac-add add-cbrt-cube flip-- fma-udef log1p-expm1-u distribute-lft-out distribute-lft-out--
2×+-commutative associate-+l- flip3-+ flip-+ difference-of-squares
Counts
4 → 126
Calls
4 calls:
2.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
3.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
86.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))
86.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
98.0ms
(- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2)))))
247.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))
246.0ms
(+ (- (- (fma 0.284496736 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))) 1.0) (* (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 3)) (/ 1 (exp (pow (fabs x) 2))))) (fma 1.061405429 (/ 1 (* (exp (pow (fabs x) 2)) (pow (+ (* 0.3275911 (fabs x)) 1.0) 5))) (* (/ (/ 1 (exp (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592))) (/ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (exp (pow (fabs x) 2))))

simplify101.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04517074
118795954
250025798

prune5.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.0b

regimes644.0ms

Accuracy

97.1% (0.1b remaining)

Error of 11.8b against oracle of 11.7b and baseline of 13.4b

bsearch241.0ms

Steps
ItersRangePoint
10
5.939545479408298e-16
0.006665254470786589
7.174100320669405e-14
9
-2.0394064324876335e-16
-6.821017948976997e-23
-1.2684304358020804e-16

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089359
191359
291359

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s3805×body160valid
618.0ms4195×body80valid