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

sample105.0ms

Algorithm

intervals

Results

42.0ms	132×	body	1024	valid
30.0ms	256×	pre	128	true
10.0ms	55×	body	512	valid
3.0ms	25×	body	256	valid
2.0ms	41×	body	128	valid
2.0ms	3×	body	2048	valid

simplify180.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

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: 13.6b

Counts

2 → 1

localize11.0ms

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))
3.4b	(tan.f64 (+.f64 y z))

rewrite23.0ms

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

series759.0ms

Counts

3 → 9

Calls

3 calls:

328.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
306.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
125.0ms	(tan.f64 (+.f64 y z))

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5091	890

prune53.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 0.2b

Counts

50 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
16.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
17.0ms	(-.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))

series2.8s

Counts

4 → 12

Calls

4 calls:

523.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
1.0s	(+.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))
183.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify77.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5275	3074

prune127.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	89	11	100
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.1b

Counts

107 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.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))
4.4b	(log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`tan-quot_binary64`
3×	`associate-r_binary64` `log-prod_binary64` `log-pow_binary64` `associate-l_binary64`
2×	`difference-of-squares_binary64` `exp-to-pow_binary64` `exp-prod_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_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` `times-frac_binary64` `flip--_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

21.0ms	(-.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))))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(-.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))
247.0ms	(exp.f64 (*.f64 (tan.f64 y) (tan.f64 z)))
182.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
332.0ms	(log.f64 (exp.f64 (*.f64 (tan.f64 y) (tan.f64 z))))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5116	1424

prune75.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	71	12	83

Merged error: 0.1b

Counts

83 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-/r_binary64` `associate-+r-_binary64` `flip3--_binary64` `cos-mult_binary64` `associate-/r/_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` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

22.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a)))
24.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a))
5.0ms	(*.f64 (sin.f64 y) (sin.f64 z))
9.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.0s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a)))
1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a))
67.0ms	(*.f64 (sin.f64 y) (sin.f64 z))
211.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))

simplify65.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5013	2712

prune76.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	86	11	97

Merged error: 0.1b

Counts

97 → 11

regimes158.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	33
1	38	33

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	4569×	body	1024	valid
524.0ms	8000×	pre	128	true
250.0ms	1383×	body	512	valid
194.0ms	198×	body	2048	valid
67.0ms	1323×	body	128	valid
64.0ms	527×	body	256	valid

Details

analyze17.0s

sample105.0ms

simplify180.0ms

prune3.0ms

localize11.0ms

rewrite23.0ms

series759.0ms

simplify66.0ms

prune53.0ms

localize16.0ms

rewrite57.0ms

series2.8s

simplify77.0ms

prune127.0ms

localize18.0ms

rewrite39.0ms

series2.0s

simplify67.0ms

prune75.0ms

localize25.0ms

rewrite69.0ms

series2.4s

simplify65.0ms

prune76.0ms

regimes158.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling