Details

Time bar (total: 24.1s)

sample400.0ms

Algorithm
intervals
Results
123.0ms110×body1280valid
60.0ms76×body640valid
54.0ms47×body1280nan
33.0ms139×body80overflowed
33.0ms38×body640nan
24.0ms42×body320valid
16.0ms22×body320nan
7.0ms19×body160valid
3.0ms8×body160nan
2.0ms10×body80valid
1.0ms8×body80nan

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
013348
145348
2276647
3500247

prune29.0ms

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

localize49.0ms

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)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
20×add-log-exp
17×distribute-lft-out
16×exp-prod
15×add-sqr-sqrt
11×associate-*r*
10×add-cube-cbrt
9×add-exp-log
7×pow1 unpow-prod-down sum-log
6×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
5×rem-exp-log
4×associate-*l* neg-log distribute-lft-out--
3×prod-exp unswap-sqr
2×associate-+l- 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
Counts
4 → 90
Calls
4 calls:
11.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
22.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))
7.0ms
(+ (- z 1.0) 1.0)

series330.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
297.0ms
(* (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)

simplify59.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0552708
12026642
25001637

prune803.0ms

Filtered
100 candidates to 68 candidates (68.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New928100
Fresh101
Picked101
Done000
Total948102

Merged error: 0.8b

Counts
102 → 8

localize51.0ms

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))

rewrite205.0ms

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×pow-prod-down neg-log
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 → 223
Calls
4 calls:
11.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
152.0ms
(* (* (* (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))))
19.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series936.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
625.0ms
(* (* (* (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))))
288.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify302.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
0374923934
1500123816

prune1.9s

Filtered
233 candidates to 140 candidates (60.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2267233
Fresh617
Picked101
Done000
Total2338241

Merged error: 0.0b

Counts
241 → 8

localize58.0ms

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))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
130×frac-times
92×*-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×div-exp
23×associate-*l/ add-cbrt-cube
17×un-div-inv
16×exp-prod
15×add-log-exp
14×pow-to-exp pow-exp
12×pow1 add-sqr-sqrt add-cube-cbrt unpow-prod-down times-frac associate-/r*
11×associate-*r*
9×cbrt-unprod
6×distribute-lft-neg-in distribute-rgt-neg-in
5×sum-log rem-exp-log
4×cbrt-undiv unpow-prod-up pow-prod-down neg-log 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 → 252
Calls
4 calls:
12.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
161.0ms
(* (* (/ (* (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))))
27.0ms
(/ (* (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))

series1.6s

Counts
4 → 10
Calls
4 calls:
21.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
1.0s
(* (* (/ (* (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))))
538.0ms
(/ (* (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))

simplify330.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (71.0ms)

IterNodesCost
0399725552
1500125377

prune1.8s

Filtered
262 candidates to 143 candidates (54.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2611262
Fresh167
Picked011
Done000
Total2628270

Merged error: 0.0b

Counts
270 → 8

localize51.0ms

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)

rewrite206.0ms

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×neg-log
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 → 270
Calls
4 calls:
16.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
148.0ms
(* (* (* (* (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))))
11.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
1.0ms
(sqrt PI)

series969.0ms

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
657.0ms
(* (* (* (* (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))))
294.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify399.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0415933224
1500333106

prune1.9s

Filtered
280 candidates to 136 candidates (48.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2782280
Fresh246
Picked101
Done011
Total2817288

Merged error: 0.0b

Counts
288 → 7

regimes110.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07950
18450
28450

end0.0ms

sample11.3s

Algorithm
intervals
Results
3.7s3329×body1280valid
2.0s2504×body640valid
1.7s1464×body1280nan
1.1s1272×body640nan
738.0ms1265×body320valid
715.0ms3834×body80overflowed
413.0ms661×body320nan
232.0ms624×body160valid
130.0ms331×body160nan
69.0ms365×body80valid
49.0ms282×body80nan