Details

analyze16.9s

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

sample120.0ms

Algorithm

intervals

Results

54.0ms	130×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	30×	body	320	valid
13.0ms	57×	body	640	valid
1.0ms	28×	body	80	valid
1.0ms	11×	body	160	valid

simplify408.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

prune20.0ms

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: 13.9b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
4.1b	(tan.f64 (+.f64 y z))

rewrite22.0ms

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:

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

series108.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
39.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
28.0ms	(tan.f64 (+.f64 y z))

simplify70.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5235	561

prune77.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 0.1b

Counts

50 → 6

localize18.0ms

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))

rewrite38.0ms

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))
13.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
13.0ms	(-.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))

series330.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
132.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
142.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
28.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify33.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4951	1271
1	4951	1271

prune113.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 0.1b

Counts

83 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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))
18.0ms	(/.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)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series282.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a))
183.0ms	(/.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)))
27.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
27.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify50.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	6633	1624

prune132.0ms

Filtered

81 candidates to 108 candidates (-33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Merged error: 0.1b

Counts

116 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `cos-mult_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 y) (sin.f64 z))
11.0ms	(/.f64 (sin.f64 y) (.f64 (cos.f64 y) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (*.f64 (cos.f64 y) (cos.f64 z))))))
9.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))
9.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 y) (sin.f64 z))
53.0ms	(/.f64 (sin.f64 y) (.f64 (cos.f64 y) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (*.f64 (cos.f64 y) (cos.f64 z))))))
28.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))
30.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))

simplify43.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4971	1310
1	4971	1310

prune89.0ms

Filtered

66 candidates to 100 candidates (-51.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	99	9	108

Merged error: 0.1b

Counts

108 → 9

regimes716.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	301	32
1	301	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3868×	body	1280	valid
536.0ms	8000×	pre	80	true
479.0ms	2008×	body	640	valid
115.0ms	676×	body	320	valid
62.0ms	1165×	body	80	valid
32.0ms	283×	body	160	valid

Details

analyze16.9s

sample120.0ms

simplify408.0ms

prune20.0ms

localize12.0ms

rewrite22.0ms

series108.0ms

simplify70.0ms

prune77.0ms

localize18.0ms

rewrite38.0ms

series330.0ms

simplify33.0ms

prune113.0ms

localize20.0ms

rewrite40.0ms

series282.0ms

simplify50.0ms

prune132.0ms

localize27.0ms

rewrite37.0ms

series123.0ms

simplify43.0ms

prune89.0ms

regimes716.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample3.2s

Profiling