Details

analyze17.3s

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

sample126.0ms

Algorithm

intervals

Results

70.0ms	131×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	66×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	11×	body	160	valid

simplify392.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

prune18.0ms

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: 12.2b

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))
3.0b	(tan.f64 (+.f64 y z))

rewrite21.0ms

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))

series115.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
37.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
29.0ms	(tan.f64 (+.f64 y z))

simplify63.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4910	561
1	4910	561

prune60.0ms

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: 0.1b

Counts

50 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64` `tan-quot_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
8×	`associate-/l/_binary64`
6×	`frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `times-frac_binary64` `flip-+_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
19.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a))
23.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
23.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
166.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6633	1624

prune102.0ms

Filtered

81 candidates to 108 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0.1b

Counts

115 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

103×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
67×	`add-cube-cbrt_binary64`
24×	`add-exp-log_binary64`
21×	`associate-l_binary64`
18×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`associate-/r/_binary64`
9×	`pow1_binary64` `div-exp_binary64`
7×	`div-inv_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `associate-/l*_binary64` `flip--_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `tan-quot_binary64`
3×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-times_binary64`

Counts

4 → 171

Calls

4 calls:

13.0ms	(.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
13.0ms	(/.f64 (cos.f64 a) (-.f64 (.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a)) (sin.f64 a)))
15.0ms	(/.f64 1 (/.f64 (cos.f64 a) (-.f64 (.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a)) (sin.f64 a))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a))
24.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
198.0ms	(/.f64 (cos.f64 a) (-.f64 (.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a)) (sin.f64 a)))
181.0ms	(/.f64 1 (/.f64 (cos.f64 a) (-.f64 (.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (cos.f64 a)) (sin.f64 a))))

simplify68.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5090	5095

prune137.0ms

Filtered

128 candidates to 183 candidates (-43.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	183	8	191

Merged error: 0.1b

Counts

191 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (tan.f64 z)) (cbrt.f64 (tan.f64 z)))
0.6b	(cbrt.f64 (tan.f64 z))
0.6b	(cbrt.f64 (tan.f64 z))
0.6b	(cbrt.f64 (tan.f64 z))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
7×	`cbrt-div_binary64` `tan-quot_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (tan.f64 z)) (cbrt.f64 (tan.f64 z)))
2.0ms	(cbrt.f64 (tan.f64 z))
2.0ms	(cbrt.f64 (tan.f64 z))
2.0ms	(cbrt.f64 (tan.f64 z))

series110.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (tan.f64 z)) (cbrt.f64 (tan.f64 z)))
24.0ms	(cbrt.f64 (tan.f64 z))
23.0ms	(cbrt.f64 (tan.f64 z))
26.0ms	(cbrt.f64 (tan.f64 z))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5354	578

prune52.0ms

Filtered

64 candidates to 91 candidates (-42.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	91	8	99

Merged error: 0.1b

Counts

99 → 8

regimes625.0ms

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	56	26
1	56	26

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3873×	body	1280	valid
552.0ms	8000×	pre	80	true
500.0ms	2038×	body	640	valid
122.0ms	718×	body	320	valid
58.0ms	1091×	body	80	valid
34.0ms	280×	body	160	valid

Details

analyze17.3s

sample126.0ms

simplify392.0ms

prune18.0ms

localize12.0ms

rewrite21.0ms

series115.0ms

simplify63.0ms

prune60.0ms

localize21.0ms

rewrite41.0ms

series250.0ms

simplify50.0ms

prune102.0ms

localize20.0ms

rewrite54.0ms

series504.0ms

simplify68.0ms

prune137.0ms

localize30.0ms

rewrite16.0ms

series110.0ms

simplify50.0ms

prune52.0ms

regimes625.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling