Details

analyze239.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample61.0ms

Algorithm

intervals

Results

30.0ms	59×	body	2560	valid
11.0ms	40×	body	1280	valid
8.0ms	48×	body	640	valid
3.0ms	75×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	365	8
1	365	8

prune2.0ms

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: 33.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 1 (cos.f64 x))
17.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 44

Calls

2 calls:

4.0ms	(-.f64 1 (cos.f64 x))
12.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(-.f64 1 (cos.f64 x))
7.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

simplify43.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4909	455
1	4909	455

prune76.0ms

Filtered

35 candidates to 50 candidates (-42.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Merged error: 0.0b

Counts

51 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
17.0b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`pow1_binary64` `associate-/l*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `div-sub_binary64` `sqr-sin-a_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
7.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))
11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))
14.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4989	1143
1	4989	1143

prune106.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	123	8	131

Merged error: 0b

Counts

131 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (sin.f64 x) x)
0.1b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log_binary64`
31×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
26×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
22×	`prod-exp_binary64`
12×	`cbrt-unprod_binary64` `div-exp_binary64`
10×	`pow1_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-*r/_binary64` `frac-times_binary64` `tan-quot_binary64`
4×	`pow-prod-down_binary64` `associate-r_binary64` `associate-*l/_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64`

Counts

3 → 110

Calls

3 calls:

4.0ms	(/.f64 (sin.f64 x) x)
14.0ms	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series35.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/.f64 (sin.f64 x) x)
14.0ms	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
17.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4966	1264
1	4966	1264

prune104.0ms

Filtered

80 candidates to 119 candidates (-48.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	120	7	127

Merged error: 0b

Counts

127 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
0.8b	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac_binary64`
54×	`add-exp-log_binary64`
46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`add-cbrt-cube_binary64`
26×	`div-exp_binary64`
16×	`associate-/r/_binary64`
14×	`associate-/r*_binary64` `cbrt-undiv_binary64`
13×	`associate-l_binary64`
12×	`tan-quot_binary64`
10×	`prod-exp_binary64`
9×	`associate-/l*_binary64`
8×	`div-inv_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 159

Calls

4 calls:

8.0ms	(/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
4.0ms	(/.f64 (sin.f64 x) x)
10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
11.0ms	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
4.0ms	(/.f64 (sin.f64 x) x)
15.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
14.0ms	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5050	2111

prune128.0ms

Filtered

117 candidates to 171 candidates (-46.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	172	6	178

Merged error: 0b

Counts

178 → 6

regimes38.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

834.0ms	1623×	body	2560	valid
342.0ms	1262×	body	1280	valid
245.0ms	1443×	body	640	valid
125.0ms	949×	body	320	valid
82.0ms	2267×	body	80	valid
38.0ms	456×	body	160	valid

Details

analyze239.0ms

sample61.0ms

simplify17.0ms

prune2.0ms

localize6.0ms

rewrite18.0ms

series9.0ms

simplify43.0ms

prune76.0ms

localize10.0ms

rewrite34.0ms

series29.0ms

simplify59.0ms

prune106.0ms

localize10.0ms

rewrite30.0ms

series35.0ms

simplify57.0ms

prune104.0ms

localize11.0ms

rewrite40.0ms

series54.0ms

simplify81.0ms

prune128.0ms

regimes38.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling