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

sample41.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
1.0ms	7×	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

prune11.0ms

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: 29.4b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 x y) z) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
28.6b	(/.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))

rewrite61.0ms

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:

7.0ms	(.f64 (+.f64 (.f64 x y) z) y)
10.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) 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))

series198.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(.f64 (+.f64 (.f64 x y) z) y)
8.0ms	(.f64 (+.f64 (.f64 (+.f64 y a) y) b) y)
16.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
164.0ms	(/.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

prune215.0ms

Filtered

85 candidates to 103 candidates (-21.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	91	12	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	13	104

Merged error: 28.3b

Counts

104 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
0.4b	(/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i))
28.2b	(.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)))

rewrite78.0ms

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`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_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×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 117

Calls

4 calls:

11.0ms	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
12.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
17.0ms	(/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i))
34.0ms	(.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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 y (+.f64 (.f64 y (+.f64 y a)) b))
16.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x y) z) y) 471841060772561/17179869184) y)
28.0ms	(/.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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4982	2919
1	4982	2919

prune182.0ms

Filtered

89 candidates to 129 candidates (-44.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	129	13	142

Merged error: 28.3b

Counts

142 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

17.9b	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
17.9b	(cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 x y) z) y) 471841060772561/17179869184))
17.9b	(cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))
28.6b	(/.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))
55.0ms	(/.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))

series291.0ms

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))
36.0ms	(cbrt.f64 (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184))
167.0ms	(/.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))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5027	2191

prune176.0ms

Filtered

72 candidates to 82 candidates (-13.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	81	14	95

Merged error: 28.3b

Counts

95 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
18.2b	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
18.2b	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
24.6b	(.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i))) (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod_binary64`
27×	`add-sqr-sqrt_binary64` `times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`cbrt-div_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `frac-times_binary64`
7×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
6×	`associate-*r/_binary64` `associate-/r/_binary64`
5×	`associate-*l/_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `associate-l_binary64` `prod-exp_binary64` `div-inv_binary64`
1×	`associate-r_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
15.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
21.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
54.0ms	(.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i))) (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
59.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
60.0ms	(cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (*.f64 y (+.f64 y a)) b)) c)) i)))
262.0ms	(.f64 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 x y) z)) 471841060772561/17179869184)) 7925469156333415/34359738368)) t) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i))) (cbrt.f64 (/.f64 1 (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 (.f64 y (+.f64 y a)) b)) c)) i)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5054	4141

prune159.0ms

Filtered

87 candidates to 114 candidates (-31.0%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	9	10
Picked	0	1	1
Done	0	3	3
Total	114	14	128

Merged error: 27.8b

Counts

128 → 14

regimes1.4s

Accuracy

0% (1.7b remaining)

Error of 29.0b against oracle of 27.3b and baseline of 29.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

708.0ms	8000×	body	80	valid
19.0ms	227×	body	80	invalid

Details

analyze2.0s

sample41.0ms

simplify168.0ms

prune11.0ms

localize27.0ms

rewrite61.0ms

series198.0ms

simplify54.0ms

prune215.0ms

localize24.0ms

rewrite78.0ms

series221.0ms

simplify67.0ms

prune182.0ms

localize32.0ms

rewrite80.0ms

series291.0ms

simplify52.0ms

prune176.0ms

localize34.0ms

rewrite109.0ms

series438.0ms

simplify57.0ms

prune159.0ms

regimes1.4s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling