Details

Time bar (total: 37.3s)

sample41.0ms

Algorithm
intervals
Results
13.0ms126×body160valid
7.0ms130×body80valid

simplify92.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08236
129236
296836
3449936
4500236

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.8b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(* (/ 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)))))
0.4b
(+ 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))))))))
13.7b
(- 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))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
15×associate-*l*
11×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1
5×flip3-+ flip-+
4×associate-/r/
3×associate-*r* associate-/r* associate-/l*
2×cbrt-undiv distribute-rgt-in frac-times associate-+r+ distribute-lft-in associate-*r/ div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×+-commutative sub-neg flip3-- frac-2neg diff-log pow-prod-down associate-*l/ clear-num sum-log *-commutative flip--
Counts
4 → 94
Calls
4 calls:
5.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
9.0ms
(* (/ 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
(+ 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))))))))) (exp (- (* (fabs x) (fabs x))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
192.0ms
(* (/ 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)))))
307.0ms
(+ 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))))))))
839.0ms
(- 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))))))

simplify106.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07472604
140362356
250012355

prune447.0ms

Filtered
106 candidates to 81 candidates (76.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New988106
Fresh000
Picked101
Done000
Total998107

Merged error: 13.7b

Counts
107 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))
0.2b
(/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
13.7b
(- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
280×times-frac
158×add-sqr-sqrt
153×add-cube-cbrt *-un-lft-identity
138×sqrt-prod
24×associate-/l*
18×associate-/r/
16×sqrt-div
15×associate-*l*
14×add-exp-log add-cbrt-cube
12×flip3-+ flip-+
9×div-inv
8×add-log-exp
6×pow1 associate-/r*
4×cbrt-undiv div-exp
3×associate-*r*
2×distribute-rgt-in frac-times associate-+r+ distribute-lft-in associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-- frac-2neg diff-log pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-- associate-/l/
Counts
4 → 256
Calls
4 calls:
9.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))
14.0ms
(/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))
30.0ms
(/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))
308.0ms
(+ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
841.0ms
(- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012776760
150026112

prune875.0ms

Filtered
268 candidates to 141 candidates (52.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2635268
Fresh527
Picked101
Done000
Total2697276

Merged error: 13.7b

Counts
276 → 7

localize40.0ms

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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
0.5b
(- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))
0.6b
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
13.7b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
49×frac-times
43×pow1
40×add-exp-log add-cbrt-cube
29×associate-*r/
24×flip3-+ flip-+
21×prod-exp cbrt-unprod
17×pow-prod-down associate-*l/
10×add-log-exp
9×distribute-rgt-in distribute-lft-in
6×cbrt-undiv div-exp associate--r+
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-sqr pow-prod-up
3×sub-neg flip3-- diff-log flip--
2×pow-plus
1×pow2 swap-sqr associate-*r* associate-*l* *-commutative difference-of-squares
Counts
4 → 126
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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
4.0ms
(- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))
17.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
3.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
303.0ms
(- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
695.0ms
(- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))
349.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
5.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify127.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0119812493
1500110883

prune607.0ms

Filtered
138 candidates to 74 candidates (53.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1362138
Fresh246
Picked101
Done000
Total1396145

Merged error: 13.7b

Counts
145 → 6

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
0.6b
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
0.7b
(pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3)
13.2b
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
107×frac-times
95×add-cbrt-cube
90×add-exp-log
88×pow1
63×associate-*r/
51×prod-exp cbrt-unprod
48×flip3-+ flip-+
40×associate-*l/
37×pow-prod-down
16×cbrt-undiv div-exp
15×add-sqr-sqrt
12×cube-div
8×distribute-rgt-in distribute-lft-in pow-sqr pow-prod-up difference-of-squares
7×*-un-lft-identity sqr-pow
6×pow-exp add-log-exp rem-cube-cbrt
5×exp-neg add-cube-cbrt
4×neg-sub0 pow-plus exp-diff
3×unpow-prod-down pow-unpow pow-pow cube-prod
2×pow2 swap-sqr associate-*r* associate-*l* *-commutative
1×difference-cubes cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 un-div-inv flip-- distribute-lft-out--
Counts
4 → 231
Calls
4 calls:
18.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
21.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
17.0ms
(pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3)
9.0ms
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3))

series22.5s

Counts
4 → 12
Calls
4 calls:
351.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
353.0ms
(* (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
1.6s
(pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3)
20.1s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))) (* (/ 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (- 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 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3))

simplify265.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0211827013
1500325709

prune1.7s

Filtered
243 candidates to 119 candidates (49.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2412243
Fresh145
Picked101
Done000
Total2436249

Merged error: 12.9b

Counts
249 → 6

regimes145.0ms

Accuracy

0% (0.1b remaining)

Error of 13.2b against oracle of 13.2b and baseline of 13.2b

bsearch0.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064318
164318

end0.0ms

sample782.0ms

Algorithm
intervals
Results
442.0ms3970×body160valid
226.0ms4030×body80valid