Details

Time bar (total: 1.3min)

sample1.9s

Algorithm
intervals
Results
1.6s127×body5120exit
104.0ms51×body1280nan
81.0ms259×body80valid
78.0ms53×body640nan
23.0ms22×body320nan
4.0ms7×body160nan
2.0ms5×body80nan

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0517487

prune17.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 2

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
1.0b
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
1.0b
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b
(sqrt (* PI 2.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
162×*-un-lft-identity
103×distribute-lft-out
27×times-frac
20×associate-*r*
16×add-sqr-sqrt
14×add-cube-cbrt
9×pow1
8×add-cbrt-cube
7×add-exp-log
6×distribute-rgt-neg-in add-log-exp
5×associate-*l*
3×flip3-+ exp-diff associate-/r* flip-+ associate-/l*
2×frac-times sqrt-pow1 associate-*r/ exp-sum pow-prod-down
1×cbrt-undiv +-commutative distribute-rgt-in sub-neg frac-2neg distribute-lft-in pow1/2 div-exp associate-*l/ frac-add prod-exp clear-num sum-log sqrt-prod *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 104
Calls
4 calls:
4.0ms
(/ PI (sin (* PI z)))
1.1s
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
39.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms
(sqrt (* PI 2.0))

series31.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(/ PI (sin (* PI z)))
19.0ms
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
5.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms
(sqrt (* PI 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050382798

prune496.0ms

Filtered
73 candidates to 114 candidates (-56.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10410114
Fresh011
Picked101
Done000
Total10511116

Merged error: 0.0b

Counts
116 → 11

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
1.0b
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b
(sqrt (* PI 2.0))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
690×*-un-lft-identity
520×distribute-lft-out
207×frac-add
117×times-frac
70×flip3-+ flip-+
62×associate-/l/
43×add-sqr-sqrt add-cube-cbrt
28×associate-/l*
26×exp-sum
8×add-cbrt-cube
7×pow1 add-exp-log associate-/r*
6×add-log-exp
4×distribute-lft-out--
2×cbrt-undiv frac-2neg sqrt-pow1 div-exp clear-num div-inv
1×+-commutative pow1/2 pow-prod-down sum-log sqrt-prod
Counts
4 → 258
Calls
4 calls:
4.0ms
(/ PI (sin (* PI z)))
149.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
32.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms
(sqrt (* PI 2.0))

series30.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(/ PI (sin (* PI z)))
18.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
5.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms
(sqrt (* PI 2.0))

simplify103.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0522614382

prune3.8s

Filtered
140 candidates to 268 candidates (-91.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2635268
Fresh6410
Picked101
Done000
Total2709279

Merged error: 0b

Counts
279 → 9

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (/ (sin (* PI z)) PI)) (* (sqrt (* PI 2.0)) (* (pow (+ (neg z) (+ 7.0 0.5)) (+ (neg z) 0.5)) (* (exp z) (/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))))))
1.0b
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b
(sqrt (* PI 2.0))

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
717×*-un-lft-identity
520×distribute-lft-out
326×add-exp-log
252×prod-exp
207×frac-add
174×times-frac
99×div-exp
81×add-cbrt-cube
70×add-sqr-sqrt add-cube-cbrt flip3-+ flip-+
62×associate-/l/
44×associate-*l*
42×cbrt-unprod
26×exp-sum
25×associate-/l*
22×rec-exp 1-exp
21×pow-to-exp pow-exp
19×cbrt-undiv
15×associate-*r/
12×pow1
6×add-log-exp
5×frac-times div-inv
4×neg-sub0 associate-+l- pow-prod-down associate-/r* distribute-lft-out-- pow-sub
3×associate-*l/
2×sqrt-pow1
1×+-commutative frac-2neg pow1/2 associate-*r* clear-num sum-log sqrt-prod associate-/r/ *-commutative
Counts
4 → 385
Calls
4 calls:
162.0ms
(* (/ 1 (/ (sin (* PI z)) PI)) (* (sqrt (* PI 2.0)) (* (pow (+ (neg z) (+ 7.0 0.5)) (+ (neg z) 0.5)) (* (exp z) (/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))))))
151.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
26.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms
(sqrt (* PI 2.0))

series91.0ms

Counts
4 → 10
Calls
4 calls:
59.0ms
(* (/ 1 (/ (sin (* PI z)) PI)) (* (sqrt (* PI 2.0)) (* (pow (+ (neg z) (+ 7.0 0.5)) (+ (neg z) 0.5)) (* (exp z) (/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))))))
27.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
5.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms
(sqrt (* PI 2.0))

simplify235.0ms

Algorithm
egg-herbie
Counts
395 → 395
Iterations

Useful iterations: 0 (106.0ms)

IterNodesCost
0542026543

prune4.3s

Filtered
178 candidates to 395 candidates (-121.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3932395
Fresh268
Picked011
Done000
Total3959404

Merged error: 0b

Counts
404 → 9

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI (/ 1 (sin (* PI z))))
1.0b
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b
(sqrt (* PI 2.0))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
691×*-un-lft-identity
520×distribute-lft-out
207×frac-add
119×times-frac
70×flip3-+ flip-+
62×associate-/l/
50×add-sqr-sqrt
43×add-cube-cbrt
26×exp-sum
25×associate-/l*
14×add-exp-log
13×associate-*r*
11×add-cbrt-cube
9×pow1
6×add-log-exp
4×prod-exp associate-/r* distribute-lft-out--
3×div-exp associate-*l* unswap-sqr
2×cbrt-undiv sqrt-pow1 pow-prod-down cbrt-unprod div-inv
1×+-commutative rec-exp frac-2neg pow1/2 1-exp associate-*r/ clear-num sum-log sqrt-prod un-div-inv *-commutative
Counts
4 → 267
Calls
4 calls:
7.0ms
(* PI (/ 1 (sin (* PI z))))
138.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
27.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms
(sqrt (* PI 2.0))

series35.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(* PI (/ 1 (sin (* PI z))))
24.0ms
(/ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
4.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms
(sqrt (* PI 2.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0527914327

prune8.5s

Filtered
142 candidates to 277 candidates (-95.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2770277
Fresh077
Picked011
Done011
Total2779286

Merged error: 0b

Counts
286 → 9

regimes94.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08183
18183

end0.0ms

sample54.2s

Algorithm
intervals
Results
45.9s3840×body5120exit
2.8s1455×body1280nan
2.5s8089×body80valid
1.7s1263×body640nan
609.0ms624×body320nan
196.0ms315×body160nan
87.0ms296×body80nan

Profiling

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