Details

analyze687.0ms

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
0%	99.8%	0.2%	8
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.9%	73.3%	0.8%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

sample33.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
2.0ms	63×	body	80	invalid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	734	13
1	734	13

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: 10.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
0.0b	(*.f64 y (-.f64 z x))
10.4b	(/.f64 (*.f64 y (-.f64 z x)) t)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_4411` `*-un-lft-identity_binary64_4426`
10×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
7×	`add-cube-cbrt_binary64_4397`
5×	`associate-r_binary64_4485` `pow1_binary64_4372` `add-log-exp_binary64_4391`
4×	`associate-*r/_binary64_4487`
3×	`associate-/r_binary64_4489` `associate-l*_binary64_4486` `times-frac_binary64_4421`
2×	`associate-/l/_binary64_4492` `div-exp_binary64_4379` `flip--_binary64_4452` `cbrt-undiv_binary64_4396` `sub-neg_binary64_4430` `prod-exp_binary64_4377` `flip3--_binary64_4425` `cbrt-unprod_binary64_4395`
1×	`distribute-rgt-in_binary64_4469` `-commutative_binary64_4494` `unswap-sqr_binary64_4454` `associate-/l_binary64_4490` `flip-+_binary64_4451` `div-inv_binary64_4427` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `distribute-lft-out--_binary64_4471` `difference-of-squares_binary64_4455` `flip3-+_binary64_4424` `pow-prod-down_binary64_4353` `distribute-lft-in_binary64_4468` `distribute-lft-out_binary64_4470` `+-commutative_binary64_4493` `sum-log_binary64_4341`

Counts

3 → 59

Calls

3 calls:

5.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
6.0ms	(*.f64 y (-.f64 z x))
7.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)

series123.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
34.0ms	(*.f64 y (-.f64 z x))
49.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)

simplify66.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5022	849

prune240.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 0.0b

Counts

69 → 5

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
0.0b	(/.f64 t (-.f64 z x))
4.9b	(/.f64 y (/.f64 t (-.f64 z x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64_4421`
105×	`*-un-lft-identity_binary64_4426`
103×	`add-sqr-sqrt_binary64_4411`
71×	`add-cube-cbrt_binary64_4397`
26×	`associate-/r*_binary64_4489`
16×	`distribute-lft-out--_binary64_4471` `difference-of-squares_binary64_4455`
11×	`associate-/r/_binary64_4491`
10×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
6×	`associate-/l*_binary64_4490` `div-inv_binary64_4427`
5×	`flip--_binary64_4452` `add-log-exp_binary64_4391` `flip3--_binary64_4425`
4×	`div-exp_binary64_4379` `cbrt-undiv_binary64_4396`
3×	`pow1_binary64_4372`
2×	`frac-2neg_binary64_4419` `clear-num_binary64_4429`
1×	`flip-+_binary64_4451` `flip3-+_binary64_4424` `distribute-lft-out_binary64_4470` `+-commutative_binary64_4493` `sum-log_binary64_4341`

Counts

3 → 151

Calls

3 calls:

19.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
5.0ms	(/.f64 t (-.f64 z x))
10.0ms	(/.f64 y (/.f64 t (-.f64 z x)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
36.0ms	(/.f64 t (-.f64 z x))
62.0ms	(/.f64 y (/.f64 t (-.f64 z x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5722	3124

prune482.0ms

Filtered

119 candidates to 160 candidates (-34.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	159	6	165

Merged error: 0b

Counts

165 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_4411`
13×	`associate-l_binary64_4486`
12×	`*-un-lft-identity_binary64_4426`
10×	`times-frac_binary64_4421` `add-cube-cbrt_binary64_4397`
7×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
5×	`associate-r_binary64_4485`
4×	`pow1_binary64_4372` `sub-neg_binary64_4430` `add-log-exp_binary64_4391`
2×	`distribute-rgt-in_binary64_4469` `frac-times_binary64_4418` `unswap-sqr_binary64_4454` `associate-*r/_binary64_4487` `associate-+r+_binary64_4477` `flip--_binary64_4452` `distribute-lft-in_binary64_4468` `prod-exp_binary64_4377` `flip3--_binary64_4425` `cbrt-unprod_binary64_4395`
1×	`-commutative_binary64_4494` `flip-+_binary64_4451` `div-inv_binary64_4427` `div-exp_binary64_4379` `distribute-lft-out--_binary64_4471` `cbrt-undiv_binary64_4396` `difference-of-squares_binary64_4455` `flip3-+_binary64_4424` `associate-l/_binary64_4488` `pow-prod-down_binary64_4353` `+-commutative_binary64_4493` `sum-log_binary64_4341`

Counts

2 → 53

Calls

2 calls:

4.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z x)))
9.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z x)))
57.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

simplify83.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5084	866

prune211.0ms

Filtered

44 candidates to 59 candidates (-34.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	59	6	65

Merged error: 0b

Counts

65 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x))))
0.0b	(/.f64 1 (-.f64 z x))
5.1b	(/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

696×	`times-frac_binary64_4421`
387×	`*-un-lft-identity_binary64_4426`
385×	`add-sqr-sqrt_binary64_4411`
293×	`add-cube-cbrt_binary64_4397`
46×	`distribute-lft-out--_binary64_4471` `difference-of-squares_binary64_4455`
38×	`div-inv_binary64_4427`
31×	`associate-/r/_binary64_4491`
26×	`associate-/r*_binary64_4489`
23×	`add-exp-log_binary64_4390`
17×	`add-cbrt-cube_binary64_4398`
16×	`associate-/l*_binary64_4490`
15×	`flip--_binary64_4452` `flip3--_binary64_4425`
12×	`div-exp_binary64_4379`
9×	`cbrt-undiv_binary64_4396`
5×	`add-log-exp_binary64_4391`
4×	`pow1_binary64_4372`
3×	`rec-exp_binary64_4378`
2×	`frac-2neg_binary64_4419` `clear-num_binary64_4429`
1×	`associate-/l/_binary64_4492` `flip-+_binary64_4451` `flip3-+_binary64_4424` `inv-pow_binary64_4348` `distribute-lft-out_binary64_4470` `+-commutative_binary64_4493` `pow-flip_binary64_4356` `sum-log_binary64_4341`

Counts

3 → 381

Calls

3 calls:

60.0ms	(+.f64 x (/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x))))
5.0ms	(/.f64 1 (-.f64 z x))
15.0ms	(/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x)))

series119.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+.f64 x (/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x))))
23.0ms	(/.f64 1 (-.f64 z x))
62.0ms	(/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

390 → 390

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5012	10666

prune836.0ms

Filtered

214 candidates to 390 candidates (-82.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	390	0	390
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	390	6	396

Merged error: 0b

Counts

396 → 6

regimes442.0ms

Accuracy

-3.5% (1.9b remaining)

Error of 1.9b against oracle of 0.0b and baseline of 1.9b

bsearch44.0ms

Steps

Iters	Range	Point
6	1486780839113475/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816	6388388370557237/24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971252983163583805434306282450321408	3.5767859404124596e-131
6	-7526216422808699/559936185544451052639360570142111069530411374308662383724997275240947967795040236345219373317901778944	-2023011618462345/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776	-8.815637691747206e-87

Iters

Range

Point

1486780839113475/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816

6388388370557237/24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971252983163583805434306282450321408

3.5767859404124596e-131

-7526216422808699/559936185544451052639360570142111069530411374308662383724997275240947967795040236345219373317901778944

-2023011618462345/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776

-8.815637691747206e-87

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	40
1	35	40

end0.0ms

sample680.0ms

Algorithm

intervals

Results

267.0ms	8000×	body	80	valid
66.0ms	1990×	body	80	invalid

Details

analyze687.0ms

sample33.0ms

simplify68.0ms

prune7.0ms

localize10.0ms

rewrite20.0ms

series123.0ms

simplify66.0ms

prune240.0ms

localize19.0ms

rewrite42.0ms

series132.0ms

simplify88.0ms

prune482.0ms

localize10.0ms

rewrite14.0ms

series102.0ms

simplify83.0ms

prune211.0ms

localize12.0ms

rewrite113.0ms

series119.0ms

simplify152.0ms

prune836.0ms

regimes442.0ms

bsearch44.0ms

simplify3.0ms

end0.0ms

sample680.0ms

Profiling