Details

Time bar (total: 25.8s)

sample437.0ms

Algorithm
intervals
Results
132.0ms110×body1280valid
70.0ms76×body640valid
59.0ms47×body1280nan
38.0ms38×body640nan
28.0ms139×body80overflowed
26.0ms42×body320valid
15.0ms22×body320nan
9.0ms19×body160valid
4.0ms8×body160nan
2.0ms10×body80valid
1.0ms8×body80nan

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
013348
145548
2279747
3500147

prune27.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 61.7b

Counts
2 → 2

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))
6.2b
(+ (- z 1.0) 1.0)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
24×add-sqr-sqrt
20×add-log-exp
17×add-cube-cbrt distribute-lft-out
16×exp-prod
11×associate-+l+ associate-*r*
9×add-exp-log prod-diff
7×pow1 unpow-prod-down sum-log
6×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
5×fma-def rem-exp-log distribute-lft-out--
4×expm1-log1p-u associate-*l* neg-log log1p-expm1-u
3×prod-exp unswap-sqr
2×associate-+l- sqrt-pow1 diff-log sqrt-prod sqr-pow
1×unpow-prod-up +-commutative neg-sub0 exp-neg pow-to-exp neg-mul-1 sub-neg distribute-neg-in flip3-+ pow1/2 exp-diff associate-*r/ exp-sum pow-prod-down pow-exp *-commutative cbrt-unprod flip-+ pow-sub difference-of-squares
Counts
4 → 112
Calls
4 calls:
11.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))
8.0ms
(+ (- z 1.0) 1.0)

series312.0ms

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
285.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))
10.0ms
(+ (- z 1.0) 1.0)

simplify71.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0595821
12411692
25001670

prune1.0s

Filtered
122 candidates to 89 candidates (73.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1148122
Fresh101
Picked101
Done000
Total1168124

Merged error: 0.8b

Counts
124 → 8

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.7b
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
130×frac-times
102×associate-*r/
82×*-un-lft-identity
56×flip3-+ flip-+
52×exp-neg associate-+l- pow-sub
51×distribute-lft-out
35×neg-sub0 exp-diff
23×associate-*l/
22×associate-*r*
21×add-exp-log
17×un-div-inv
16×add-sqr-sqrt exp-prod
15×prod-exp add-cbrt-cube add-log-exp
12×pow1
11×add-cube-cbrt
7×unpow-prod-down cbrt-unprod
6×distribute-lft-neg-in distribute-rgt-neg-in
5×associate-*l* sum-log rem-exp-log
4×expm1-log1p-u pow-prod-down neg-log log1p-expm1-u
3×distribute-lft-out-- unswap-sqr
2×pow-to-exp sqrt-pow1 pow-exp sqrt-prod *-commutative sqr-pow
1×unpow-prod-up distribute-rgt-in neg-mul-1 distribute-neg-in distribute-lft-in pow1/2 diff-log exp-sum
Counts
4 → 231
Calls
4 calls:
11.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
150.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
6.0ms
(sqrt (* PI 2.0))

series1.1s

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
822.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
298.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify313.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0385223664
1500223540

prune1.8s

Filtered
241 candidates to 148 candidates (61.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2356241
Fresh617
Picked101
Done000
Total2427249

Merged error: 0.0b

Counts
249 → 7

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.7b
(* (* (/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
130×frac-times
104×*-un-lft-identity
72×add-exp-log
56×flip3-+ flip-+ distribute-lft-out
52×exp-neg
50×associate-*r/
45×prod-exp
35×neg-sub0 exp-diff
24×add-sqr-sqrt add-cube-cbrt div-exp
23×associate-*l/ add-cbrt-cube
22×unpow-prod-up
21×times-frac associate-/r*
18×prod-diff
17×un-div-inv
16×exp-prod
15×add-log-exp
14×pow-to-exp pow-exp
12×pow1 unpow-prod-down
11×associate-*r*
9×cbrt-unprod
6×distribute-lft-neg-in distribute-rgt-neg-in
5×sum-log rem-exp-log
4×cbrt-undiv expm1-log1p-u pow-prod-down neg-log log1p-expm1-u distribute-lft-out--
2×sub-neg sqrt-pow1 sqr-pow
1×distribute-rgt-in neg-mul-1 distribute-neg-in frac-2neg distribute-lft-in pow1/2 diff-log associate-*l* exp-sum clear-num sqrt-prod associate-/r/ *-commutative div-inv associate-/l* pow-sub
Counts
4 → 278
Calls
4 calls:
10.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
157.0ms
(* (* (/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
34.0ms
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
3.0ms
(sqrt (* PI 2.0))

series1.4s

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
850.0ms
(* (* (/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
539.0ms
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify317.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0424225715
1500125694

prune2.2s

Filtered
288 candidates to 170 candidates (59.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2880288
Fresh066
Picked011
Done000
Total2887295

Merged error: 0.0b

Counts
295 → 7

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.7b
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI)) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
560×frac-add
212×frac-times
173×exp-neg
147×associate-*l/
104×mul-1-neg
102×associate-*r/
80×flip3-+ flip-+
73×*-un-lft-identity
69×un-div-inv
52×neg-sub0 exp-diff
46×distribute-lft-out
24×pow1
23×add-cbrt-cube
18×add-exp-log
17×associate-*r*
16×exp-prod
15×add-log-exp
13×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
11×add-cube-cbrt
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×sum-log rem-exp-log
4×expm1-log1p-u neg-log log1p-expm1-u
2×associate-*l* *-commutative distribute-lft-out--
1×distribute-rgt-in neg-mul-1 rem-sqrt-square distribute-neg-in distribute-lft-in sqrt-pow1 pow1/2 diff-log exp-sum
Counts
4 → 278
Calls
4 calls:
16.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
146.0ms
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI)) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
15.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
2.0ms
(sqrt PI)

series963.0ms

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
647.0ms
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI)) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
298.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify382.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 1 (67.0ms)

IterNodesCost
0426232787
1500132778

prune2.1s

Filtered
288 candidates to 145 candidates (50.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2871288
Fresh145
Picked101
Done011
Total2896295

Merged error: 0.0b

Counts
295 → 6

regimes89.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07950
18450
28450

end0.0ms

sample12.2s

Algorithm
intervals
Results
4.0s3329×body1280valid
2.2s2504×body640valid
1.9s1464×body1280nan
1.2s1272×body640nan
799.0ms1265×body320valid
794.0ms3834×body80overflowed
470.0ms661×body320nan
254.0ms624×body160valid
147.0ms331×body160nan
78.0ms365×body80valid
51.0ms282×body80nan