Details

analyze16.6s

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

sample123.0ms

Algorithm

intervals

Results

52.0ms	119×	body	1280	valid
31.0ms	256×	pre	80	true
17.0ms	65×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	34×	body	80	valid
2.0ms	12×	body	160	valid

simplify505.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	187	14
1	187	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: 13.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
2.3b	(tan.f64 (+.f64 y z))

rewrite29.0ms

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)))
8.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
6.0ms	(tan.f64 (+.f64 y z))

series409.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
154.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
81.0ms	(tan.f64 (+.f64 y z))

simplify79.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4975	890
1	4975	890

prune56.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite45.0ms

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))
17.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
15.0ms	(+.f64 x (-.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))

series1.3s

Counts

4 → 12

Calls

4 calls:

98.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
573.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
577.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
102.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify59.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5041	2073

prune95.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
0.2b	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
0.3b	(*.f64 (tan.f64 z) (sin.f64 y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
4×	`times-frac_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-+r-_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

23.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
22.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
7.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
6.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

series1.4s

Counts

4 → 12

Calls

4 calls:

597.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
610.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
110.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
71.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

simplify92.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4969	2412
1	4969	2412

prune90.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 0.1b

Counts

94 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))))) (tan.f64 a)))
0.2b	(exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))
2.9b	(log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`tan-quot_binary64`
3×	`associate-r_binary64` `log-prod_binary64` `log-pow_binary64` `associate-l_binary64`
2×	`distribute-lft-out_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

21.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))))) (tan.f64 a)))
4.0ms	(exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
2.0ms	(log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z))))

series890.0ms

Counts

4 → 12

Calls

4 calls:

552.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))))) (tan.f64 a)))
136.0ms	(exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))
99.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
103.0ms	(log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z))))

simplify77.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5534	1432

prune49.0ms

Filtered

50 candidates to 73 candidates (-46.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 0.1b

Counts

83 → 10

regimes224.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	33
1	39	33

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3860×	body	1280	valid
538.0ms	8000×	pre	80	true
479.0ms	1996×	body	640	valid
109.0ms	680×	body	320	valid
64.0ms	1205×	body	80	valid
36.0ms	259×	body	160	valid

Details

analyze16.6s

sample123.0ms

simplify505.0ms

prune3.0ms

localize12.0ms

rewrite29.0ms

series409.0ms

simplify79.0ms

prune56.0ms

localize15.0ms

rewrite45.0ms

series1.3s

simplify59.0ms

prune95.0ms

localize21.0ms

rewrite60.0ms

series1.4s

simplify92.0ms

prune90.0ms

localize18.0ms

rewrite35.0ms

series890.0ms

simplify77.0ms

prune49.0ms

regimes224.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample3.2s

Profiling