Details

analyze647.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	63×	body	80	invalid

simplify215.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (213.0ms)

Iter	Nodes	Cost
0	1483	11
1	1483	11

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 3.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(/.f64 t (-.f64 1 z))
3.3b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
12×	`distribute-lft-out--_binary64`
10×	`associate-r_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 90

Calls

3 calls:

22.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))
25.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series36.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))
20.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify54.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5441	1135

prune91.0ms

Filtered

72 candidates to 99 candidates (-37.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 0.0b

Counts

100 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

3.3b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
6.9b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
6.9b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
6.9b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
12×	`associate-*r/_binary64`
10×	`associate-r_binary64`
9×	`cbrt-div_binary64`
8×	`times-frac_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

26.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
22.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
24.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
22.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
63.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
65.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
62.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5126	1103

prune92.0ms

Filtered

64 candidates to 78 candidates (-21.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	78	9	87

Merged error: 0.0b

Counts

87 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.8b	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
1.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-l_binary64`
10×	`cbrt-prod_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
8×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`associate-*r/_binary64`
2×	`flip3--_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
31.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
31.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 x)
18.0ms	(cbrt.f64 x)
38.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
23.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5233	962

prune62.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 x))
0.9b	(.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))
1.2b	(.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x)))
1.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1_binary64` `add-exp-log_binary64`
33×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
25×	`add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
18×	`cbrt-prod_binary64`
15×	`associate-*l/_binary64`
12×	`associate-l_binary64`
11×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64`
8×	`times-frac_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`flip3--_binary64` `associate-r/_binary64` `flip--_binary64` `frac-sub_binary64` `-commutative_binary64`
1×	`pow1/3_binary64` `unswap-sqr_binary64`

Counts

4 → 110

Calls

4 calls:

2.0ms	(cbrt.f64 (cbrt.f64 x))
30.0ms	(.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))
36.0ms	(.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x)))
41.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt.f64 (cbrt.f64 x))
65.0ms	(.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))
41.0ms	(.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x)))
23.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5063	1694

prune54.0ms

Filtered

78 candidates to 122 candidates (-56.4%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	122	10	132

Merged error: 0.0b

Counts

132 → 10

regimes478.0ms

Accuracy

72% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 4.5b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	83	55
1	83	55

end0.0ms

sample640.0ms

Algorithm

intervals

Results

300.0ms	8000×	body	80	valid
70.0ms	1898×	body	80	invalid

Details

analyze647.0ms

sample24.0ms

simplify215.0ms

prune7.0ms

localize8.0ms

rewrite57.0ms

series36.0ms

simplify54.0ms

prune91.0ms

localize13.0ms

rewrite98.0ms

series210.0ms

simplify67.0ms

prune92.0ms

localize11.0ms

rewrite68.0ms

series94.0ms

simplify41.0ms

prune62.0ms

localize18.0ms

rewrite113.0ms

series152.0ms

simplify69.0ms

prune54.0ms

regimes478.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample640.0ms

Profiling