Details

analyze1.1s

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample33.0ms

Algorithm

intervals

Results

8.0ms	214×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	28×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	160	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

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: 12.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
3.6b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
5.0b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
18.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series122.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
60.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
45.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5183	1602

prune173.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	115	13	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 3.8b

Counts

129 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
1.9b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.2b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
46×	`associate-r_binary64`
37×	`cbrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
39.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
5.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt.f64 (-.f64 a z))
40.0ms	(cbrt.f64 (-.f64 a z))
72.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
64.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5292	2530

prune162.0ms

Filtered

110 candidates to 146 candidates (-32.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	146	13	159

Merged error: 3.5b

Counts

159 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
1.0b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))))
7.8b	(+.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-div_binary64`
25×	`add-exp-log_binary64`
20×	`flip3--_binary64` `flip--_binary64` `frac-times_binary64`
17×	`associate-l_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`-un-lft-identity_binary64` `associate-r/_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`cbrt-prod_binary64`
9×	`pow1_binary64`
8×	`add-cube-cbrt_binary64` `associate-/r/_binary64`
7×	`associate-*l/_binary64`
6×	`add-log-exp_binary64` `times-frac_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`pow1/3_binary64` `unswap-sqr_binary64`
1×	`flip3-+_binary64` `associate-r_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 a z))
4.0ms	(cbrt.f64 (-.f64 a z))
27.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))))
5.0ms	(+.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt.f64 (-.f64 a z))
28.0ms	(cbrt.f64 (-.f64 a z))
238.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))))
68.0ms	(+.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5727	2209

prune136.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	112	13	125

Merged error: 3.5b

Counts

125 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 a z))
0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
4.8b	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
5.0b	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

8.0ms	(/.f64 1 (-.f64 a z))
14.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
5.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
17.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 a z))
15.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
63.0ms	(+.f64 x (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))))
43.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5717	1769

prune100.0ms

Filtered

98 candidates to 158 candidates (-61.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	158	13	171

Merged error: 3.5b

Counts

171 → 13

regimes535.0ms

Accuracy

24.4% (6.8b remaining)

Error of 10.3b against oracle of 3.5b and baseline of 12.4b

bsearch63.0ms

Steps

Iters	Range		Point
9	6.993586934865164e-116	5.485377558850572e-107	1.2161147335711477e-113
10	-8.727727116639551e-172	-8.488667879315993e-182	-4.807158068872457e-172

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	78
1	73	78

end0.0ms

sample819.0ms

Algorithm

intervals

Results

271.0ms	6525×	body	80	valid
86.0ms	543×	body	640	valid
50.0ms	271×	body	1280	valid
47.0ms	391×	body	320	valid
46.0ms	1181×	body	80	invalid
23.0ms	256×	body	160	valid
3.0ms	14×	body	2560	valid

Details

analyze1.1s

sample33.0ms

simplify82.0ms

prune4.0ms

localize9.0ms

rewrite35.0ms

series122.0ms

simplify47.0ms

prune173.0ms

localize13.0ms

rewrite57.0ms

series203.0ms

simplify43.0ms

prune162.0ms

localize20.0ms

rewrite44.0ms

series362.0ms

simplify43.0ms

prune136.0ms

localize10.0ms

rewrite49.0ms

series127.0ms

simplify49.0ms

prune100.0ms

regimes535.0ms

bsearch63.0ms

simplify2.0ms

end0.0ms

sample819.0ms

Profiling