Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

sample45.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
1.0ms	8×	body	80	invalid

simplify168.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (165.0ms)

Iter	Nodes	Cost
0	4834	33
1	4834	33

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.8b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
0.1b	(.f64 (+.f64 (.f64 x y) z) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
29.1b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64` `times-frac_binary64`
6×	`associate-*l/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 91

Calls

4 calls:

12.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
7.0ms	(.f64 (+.f64 (.f64 x y) z) y)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
29.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

series214.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
9.0ms	(.f64 (+.f64 (.f64 x y) z) y)
18.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
178.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5078	2160

prune189.0ms

Filtered

85 candidates to 103 candidates (-21.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	14	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 28.8b

Counts

104 → 14

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 x y) z) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
0.6b	(/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i))
28.4b	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64` `add-exp-log_binary64`
20×	`times-frac_binary64`
15×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`associate-l_binary64`
6×	`flip3-+_binary64` `prod-exp_binary64` `flip-+_binary64` `associate-*l/_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `frac-times_binary64`
1×	`associate-*r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 115

Calls

4 calls:

10.0ms	(.f64 (+.f64 (.f64 x y) z) y)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
15.0ms	(/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i))
40.0ms	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (+.f64 (.f64 x y) z) y)
17.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
32.0ms	(/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i))
168.0ms	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184) y) 7925469156333415/34359738368) y) t) (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5273	2857

prune136.0ms

Filtered

89 candidates to 127 candidates (-42.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	127	14	141

Merged error: 28.8b

Counts

141 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

17.6b	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
17.6b	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
17.6b	(cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))
29.1b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))) (.f64 y (cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`cbrt-div_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 70

Calls

4 calls:

8.0ms	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
8.0ms	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
8.0ms	(cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))
56.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))) (.f64 y (cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

series334.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
43.0ms	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
40.0ms	(cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))
206.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))) (.f64 y (cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5027	2191

prune140.0ms

Filtered

70 candidates to 82 candidates (-17.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	82	14	96

Merged error: 28.8b

Counts

96 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

20.0b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
20.0b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
20.0b	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
29.1b	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
6×	`cbrt-div_binary64` `associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64` `cbrt-prod_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 64

Calls

4 calls:

10.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
10.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
9.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
38.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

series286.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
47.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
48.0ms	(cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 x y) z)) 471841060772561/17179869184)))
142.0ms	(/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) (cbrt.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)))) 7925469156333415/34359738368) y) t) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

simplify49.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4979	2089
1	4979	2089

prune80.0ms

Filtered

70 candidates to 76 candidates (-8.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	75	15	90

Merged error: 28.8b

Counts

90 → 15

regimes1.1s

Accuracy

0% (1.1b remaining)

Error of 29.5b against oracle of 28.4b and baseline of 29.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	35
1	45	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

719.0ms	8000×	body	80	valid
20.0ms	241×	body	80	invalid

Details

analyze2.0s

sample45.0ms

simplify168.0ms

prune9.0ms

localize22.0ms

rewrite63.0ms

series214.0ms

simplify54.0ms

prune189.0ms

localize41.0ms

rewrite80.0ms

series226.0ms

simplify50.0ms

prune136.0ms

localize31.0ms

rewrite80.0ms

series334.0ms

simplify50.0ms

prune140.0ms

localize28.0ms

rewrite68.0ms

series286.0ms

simplify49.0ms

prune80.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling