Details

Time bar (total: 17.3s)

sample57.0ms

Algorithm
intervals
Results
29.0ms120×body160valid
17.0ms136×body80valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0507263

prune9.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 13.1b

Counts
2 → 1

localize26.0ms

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))))))))
13.1b
(- 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)))))))) (pow (exp (fabs x)) (fabs x)))))

rewrite18.0ms

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 add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv associate-+r+ frac-2neg div-exp clear-num div-inv
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log sum-log flip--
Counts
4 → 83
Calls
4 calls:
5.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
5.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
3.0ms
(+ 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))))))))
3.0ms
(- 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)))))))) (pow (exp (fabs x)) (fabs x)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
8.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
71.0ms
(+ 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))))))))
295.0ms
(- 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)))))))) (pow (exp (fabs x)) (fabs x)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
050212932

prune364.0ms

Filtered
72 candidates to 95 candidates (-31.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh000
Picked101
Done000
Total92496

Merged error: 13.1b

Counts
96 → 4

localize42.0ms

Local error

Found 4 expressions with local error:

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))))))))
0.5b
(* (/ (+ 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 (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
0.7b
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
12.6b
(- (pow 1.0 3) (pow (* (/ 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 (pow (fabs x) 2)))) 3))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×add-cbrt-cube
19×add-exp-log
15×*-un-lft-identity
13×add-cube-cbrt associate-*l*
10×times-frac
9×pow1
8×add-log-exp difference-of-squares
7×sqr-pow
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp pow-exp rem-cube-cbrt
3×cube-div frac-times unpow-prod-down pow-unpow flip3-+ cube-prod associate-*r/ associate-*r* flip-+
2×distribute-rgt-in associate-+r+ pow-pow distribute-lft-in pow-prod-down associate-*l/ unswap-sqr
1×difference-cubes +-commutative cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 sum-log *-commutative flip-- div-inv distribute-lft-out--
Counts
4 → 104
Calls
4 calls:
3.0ms
(+ 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))))))))
12.0ms
(* (/ (+ 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)))))))) (exp (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
13.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
9.0ms
(- (pow 1.0 3) (pow (* (/ 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 (pow (fabs x) 2)))) 3))

series1.5s

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ 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))))))))
379.0ms
(* (/ (+ 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)))))))) (exp (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
187.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
835.0ms
(- (pow 1.0 3) (pow (* (/ 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 (pow (fabs x) 2)))) 3))

simplify86.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0498610980
1498610980

prune2.6s

Filtered
85 candidates to 116 candidates (-36.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1133116
Fresh123
Picked101
Done000
Total1155120

Merged error: 12.4b

Counts
120 → 5

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (+ 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 (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
0.7b
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
0.7b
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
12.6b
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
35×add-cbrt-cube
30×add-exp-log
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
13×associate-*l*
12×pow1
10×times-frac pow-exp prod-exp cbrt-unprod rem-cube-cbrt
9×cbrt-undiv div-exp
6×cube-div pow-unpow add-log-exp
4×frac-times pow-pow associate-*r/ difference-of-squares
3×unpow-prod-down cube-prod associate-*r* pow-prod-down associate-*l/ sqr-pow
2×cube-mult pow-to-exp flip3-+ unpow3 flip-+ unswap-sqr
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log *-commutative flip-- div-inv
Counts
4 → 116
Calls
4 calls:
12.0ms
(* (/ (+ 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)))))))) (exp (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
13.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
13.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
9.0ms
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3))))

series1.6s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (/ (+ 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)))))))) (exp (pow (fabs x) 2))) (+ 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 (pow (fabs x) 2))))))
187.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
187.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
834.0ms
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3))))

simplify91.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0499311093
1499311093

prune3.9s

Filtered
88 candidates to 128 candidates (-45.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1271128
Fresh134
Picked101
Done000
Total1294133

Merged error: 12.4b

Counts
133 → 4

localize76.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x))))))
0.7b
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
0.8b
(pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3)
12.6b
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (* 1.0 (/ (pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3) (pow (* (+ 1.0 (* 0.3275911 (fabs x))) (exp (pow (fabs x) 2))) 3))))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
20×add-sqr-sqrt
18×add-cbrt-cube distribute-lft-out
16×add-exp-log
11×add-log-exp
9×unpow-prod-down
8×pow1 add-cube-cbrt cube-prod
7×cube-div times-frac distribute-lft-out--
6×pow-unpow pow-exp rem-cube-cbrt
5×difference-of-squares
4×cbrt-undiv div-exp prod-exp cbrt-unprod
3×pow-pow flip3-+ diff-log frac-add frac-sub flip-+ sqr-pow
2×cube-mult pow-to-exp sub-neg flip3-- unpow3 flip--
1×frac-times associate-*r/ pow-prod-down associate-*l/ sum-log associate--r+ unpow2
Counts
4 → 103
Calls
4 calls:
51.0ms
(- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x))))))
13.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
70.0ms
(pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3)
84.0ms
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (* 1.0 (/ (pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3) (pow (* (+ 1.0 (* 0.3275911 (fabs x))) (exp (pow (fabs x) 2))) 3))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x))))))
186.0ms
(pow (* (/ 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 (pow (fabs x) 2)))) 3)
117.0ms
(pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3)
652.0ms
(- (pow 1.0 3) (* (sqrt (pow (* (/ 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 (pow (fabs x) 2)))) 3)) (sqrt (* 1.0 (/ (pow (+ (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 4)) (+ 0.254829592 (- (/ 1.421413741 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2)) (+ (/ 1.453152027 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3)) (/ 0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))))) 3) (pow (* (+ 1.0 (* 0.3275911 (fabs x))) (exp (pow (fabs x) 2))) 3))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049938329
149938329

prune3.3s

Filtered
72 candidates to 115 candidates (-59.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1123115
Fresh123
Picked101
Done000
Total1145119

Merged error: 12.2b

Counts
119 → 5

regimes213.0ms

Accuracy

0% (0.0b remaining)

Error of 13.0b against oracle of 12.9b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
091525
191525

end0.0ms

sample1.6s

Algorithm
intervals
Results
952.0ms3940×body160valid
505.0ms4060×body80valid

Profiling

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