Details

analyze17.0s

Algorithm

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

sample116.0ms

Algorithm

intervals

Results

63.0ms	161×	body	1024	valid
18.0ms	256×	pre	128	true
9.0ms	6×	body	2048	valid
8.0ms	40×	body	512	valid
2.0ms	15×	body	256	valid
2.0ms	34×	body	128	valid

simplify175.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	186	14
1	186	14

prune3.0ms

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: 16.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
5.0b	(tan.f64 (+.f64 y z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`tan-quot_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

3 → 40

Calls

3 calls:

6.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
15.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
7.0ms	(tan.f64 (+.f64 y z))

series769.0ms

Counts

3 → 9

Calls

3 calls:

333.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
294.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
141.0ms	(tan.f64 (+.f64 y z))

simplify65.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5091	890

prune55.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Merged error: 0.1b

Counts

50 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `times-frac_binary64` `flip--_binary64` `associate-+r+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
19.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
15.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.5s

Counts

4 → 12

Calls

4 calls:

198.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
1.1s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
179.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5057	2073

prune106.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	11	77
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	74	12	86

Merged error: 0.1b

Counts

86 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
2.3b	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
17×	`add-log-exp_binary64`
14×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`tan-quot_binary64` `exp-prod_binary64`
4×	`distribute-lft-out_binary64` `sum-log_binary64`
3×	`diff-log_binary64` `associate-r_binary64` `associate-l_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `associate-+l-_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-+l+_binary64` `exp-diff_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `times-frac_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 69

Calls

4 calls:

19.0ms	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
15.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
21.0ms	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

series4.7s

Counts

4 → 12

Calls

4 calls:

2.0s	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
195.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
1.4s	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5115	2396

prune93.0ms

Filtered

59 candidates to 81 candidates (-37.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	81	12	93

Merged error: 0.1b

Counts

93 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 z) (cos.f64 y))
0.2b	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.2b	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`tan-quot_binary64`
4×	`times-frac_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cos-mult_binary64` `associate-r/_binary64` `frac-add_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 80

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 z) (cos.f64 y))
23.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
11.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))

series1.6s

Counts

4 → 12

Calls

4 calls:

66.0ms	(*.f64 (sin.f64 z) (cos.f64 y))
1.1s	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
182.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
303.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5618	2629

prune88.0ms

Filtered

70 candidates to 92 candidates (-31.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	92	12	104

Merged error: 0.1b

Counts

104 → 12

regimes157.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	33
1	54	33

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4538×	body	1024	valid
520.0ms	8000×	pre	128	true
259.0ms	1381×	body	512	valid
199.0ms	209×	body	2048	valid
72.0ms	1342×	body	128	valid
63.0ms	530×	body	256	valid

Details

analyze17.0s

sample116.0ms

simplify175.0ms

prune3.0ms

localize13.0ms

rewrite32.0ms

series769.0ms

simplify65.0ms

prune55.0ms

localize17.0ms

rewrite51.0ms

series2.5s

simplify52.0ms

prune106.0ms

localize20.0ms

rewrite68.0ms

series4.7s

simplify68.0ms

prune93.0ms

localize29.0ms

rewrite55.0ms

series1.6s

simplify61.0ms

prune88.0ms

regimes157.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling