Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

sample30.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5060	17

prune4.0ms

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: 19.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (*.f64 z (-.f64 b y)))
0.0b	(*.f64 z (-.f64 t a))
1.0b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
18.9b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`sub-neg_binary64` `pow1_binary64`
5×	`associate-r_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `associate-+r+_binary64`
3×	`associate-/r_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(+.f64 y (*.f64 z (-.f64 b y)))
7.0ms	(*.f64 z (-.f64 t a))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
9.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

series132.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 y (*.f64 z (-.f64 b y)))
8.0ms	(*.f64 z (-.f64 t a))
16.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
100.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5375	1289

prune102.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 19.1b

Counts

94 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 t a))
0.3b	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
1.0b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
18.8b	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
18×	`associate-/r*_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/r/_binary64`
8×	`div-exp_binary64`
7×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`associate-r_binary64`
4×	`sub-neg_binary64` `cbrt-undiv_binary64`
3×	`associate-l_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 152

Calls

4 calls:

7.0ms	(*.f64 z (-.f64 t a))
10.0ms	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
9.0ms	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 z (-.f64 t a))
185.0ms	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
15.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
91.0ms	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))

simplify67.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5104	3633

prune108.0ms

Filtered

112 candidates to 164 candidates (-46.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	162	13	175

Merged error: 19.1b

Counts

175 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 t a))
0.3b	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
1.0b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
18.7b	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`associate-r_binary64` `times-frac_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `div-inv_binary64` `associate-+r+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 112

Calls

4 calls:

7.0ms	(*.f64 z (-.f64 t a))
5.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
12.0ms	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 z (-.f64 t a))
19.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
16.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
100.0ms	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5992	1663

prune88.0ms

Filtered

79 candidates to 124 candidates (-57.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	124	13	137

Merged error: 19.1b

Counts

137 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
1.0b	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z))))
18.9b	(/.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z)))) (+.f64 y (*.f64 z (-.f64 b y))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
4×	`pow1_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
5.0ms	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z))))
10.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z)))) (+.f64 y (*.f64 z (-.f64 b y))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 z)
16.0ms	(cbrt.f64 z)
23.0ms	(+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z))))
113.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 t a) (cbrt.f64 z)))) (+.f64 y (*.f64 z (-.f64 b y))))

simplify52.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4974	1053
1	4974	1053

prune34.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	76	13	89

Merged error: 19.1b

Counts

89 → 13

regimes757.0ms

Accuracy

0% (0.7b remaining)

Error of 23.5b against oracle of 22.7b and baseline of 23.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms

sample738.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
22.0ms	442×	body	80	invalid

Details

analyze1.4s

sample30.0ms

simplify60.0ms

prune4.0ms

localize12.0ms

rewrite26.0ms

series132.0ms

simplify42.0ms

prune102.0ms

localize13.0ms

rewrite36.0ms

series298.0ms

simplify67.0ms

prune108.0ms

localize13.0ms

rewrite33.0ms

series144.0ms

simplify63.0ms

prune88.0ms

localize16.0ms

rewrite20.0ms

series167.0ms

simplify52.0ms

prune34.0ms

regimes757.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample738.0ms

Profiling