Details

Time bar (total: 10.4s)

sample43.0ms

Algorithm
intervals
Results
13.0ms116×body160valid
8.0ms140×body80valid

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
08236
131036
2105431
3485530
4500130
done500130

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.4b
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
12.7b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
add-exp-log add-cbrt-cube add-log-exp
associate-/r* associate-/l*
pow1 expm1-log1p-u associate-/r/ log1p-expm1-u
fma-def flip3-+ fma-neg prod-diff flip-+
cbrt-undiv associate-+r+ frac-2neg div-exp clear-num div-inv
+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log sum-log flip--
Counts
4 → 100
Calls
4 calls:
8.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
9.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
6.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
7.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
31.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
295.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
814.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify71.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04752423
122542059
250021979
done50021979

prune511.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
0.6b
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
1.5b
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
12.7b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
57×add-sqr-sqrt *-un-lft-identity
55×add-cube-cbrt
24×unpow-prod-down
22×add-exp-log
20×associate-/r*
12×cube-prod div-exp prod-diff
add-cbrt-cube add-log-exp sqr-pow
pow-to-exp rec-exp fma-neg 1-exp pow-exp associate-/l*
pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u unpow2
cbrt-undiv cube-div sub-neg flip3-- pow-flip frac-2neg diff-log clear-num associate-/r/ flip-- fma-udef div-inv inv-pow
flip3-+ associate--l+ flip-+ associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 186
Calls
4 calls:
26.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
25.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
7.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
6.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
63.0ms
(/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
196.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
505.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))))

simplify113.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06703792
133972822
250012756
done50012756

prune750.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.7b

localize70.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
1.5b
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
1.5b
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) 1.453152027 (/ (* 0.284496736 1) (fma 0.3275911 (fabs x) 1.0))))
12.2b
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))) 3))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
123×prod-diff
80×add-sqr-sqrt
72×*-un-lft-identity
64×add-cube-cbrt
41×unpow-prod-down cube-prod
27×sqr-pow
21×cube-mult fma-neg unpow3
12×add-log-exp
11×difference-of-squares
fma-udef
pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out--
associate--l+ associate--r+
difference-cubes
Counts
4 → 222
Calls
4 calls:
6.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
6.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
7.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) 1.453152027 (/ (* 0.284496736 1) (fma 0.3275911 (fabs x) 1.0))))
27.0ms
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
200.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
200.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0)))))
196.0ms
(- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) 1.453152027 (/ (* 0.284496736 1) (fma 0.3275911 (fabs x) 1.0))))
766.0ms
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (- (fma 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (fma 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (* 0.284496736 (/ 1 (+ (* 0.3275911 (fabs x)) 1.0))))))) (exp (- (* (fabs x) (fabs x))))) 3))

simplify282.0ms

Counts
234 → 234
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
098317077
1393011950
2500111926
done500111926

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0))
0.4b
(fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
12.7b
(- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))
12.7b
(log (exp (- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
42×prod-diff
39×add-sqr-sqrt *-un-lft-identity
35×add-cube-cbrt
26×log-prod
23×exp-sum
21×times-frac
add-exp-log add-cbrt-cube
div-inv
log-pow add-log-exp
pow1 exp-prod
expm1-log1p-u log1p-expm1-u
fma-neg associate-/r*
cbrt-undiv sub-neg div-exp distribute-lft-out-- difference-of-squares
log-div flip3-- frac-2neg exp-diff diff-log rem-log-exp prod-exp clear-num flip-- cbrt-unprod fma-udef associate-/l*
Counts
4 → 116
Calls
4 calls:
9.0ms
(/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0))
0.0ms
(fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
18.0ms
(- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))
47.0ms
(log (exp (- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0))
216.0ms
(fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
402.0ms
(- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))
398.0ms
(log (exp (- 1.0 (/ (* (/ (* (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) 1) (exp (pow (fabs x) 2))))))

simplify120.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06108463
125015264
250015206
done50015206

prune519.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.7b

regimes150.0ms

Accuracy

0% (0.0b remaining)

Error of 13.9b against oracle of 13.9b and baseline of 13.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05397
15597
25597
done5597

end0.0ms

sample814.0ms

Algorithm
intervals
Results
440.0ms3940×body160valid
231.0ms4060×body80valid