Details

analyze244.0ms

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

sample56.0ms

Algorithm

intervals

Results

18.0ms	36×	body	2560	valid
11.0ms	41×	body	1280	valid
9.0ms	53×	body	640	valid
8.0ms	27×	body	320	valid
3.0ms	81×	body	80	valid
2.0ms	18×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	367	12
1	367	12

prune1.0ms

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: 29.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(-.f64 1 (cos.f64 x))
12.0b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite13.0ms

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))
8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series43.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(-.f64 1 (cos.f64 x))
32.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

simplify73.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5892	700

prune55.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
11.8b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite31.0ms

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)))
5.0ms	(*.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))

series138.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
17.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
6.0ms	(+.f64 1 (cos.f64 x))
69.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

simplify120.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4930	1781
1	4930	1781

prune84.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 0b

Counts

131 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac_binary64`
858×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
108×	`div-inv_binary64`
60×	`associate-/r*_binary64`
40×	`add-exp-log_binary64`
31×	`add-cbrt-cube_binary64`
28×	`div-exp_binary64`
19×	`cbrt-undiv_binary64` `associate-/l*_binary64`
16×	`associate-/r/_binary64`
3×	`add-log-exp_binary64` `pow1_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64`
1×	`tan-quot_binary64`

Counts

3 → 754

Calls

3 calls:

6.0ms	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
22.0ms	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
49.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
84.0ms	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

simplify353.0ms

Algorithm

egg-herbie

Counts

763 → 763

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4946	30522
1	4946	30522

prune671.0ms

Filtered

412 candidates to 763 candidates (-85.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	763	0	763
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	763	6	769

Merged error: 0b

Counts

769 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x)
0.6b	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
11.1b	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))
11.1b	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
17×	`pow1_binary64`
16×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r*_binary64` `tan-quot_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64`
1×	`associate-/l/_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 132

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x)
15.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
4.0ms	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))
4.0ms	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x)
69.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
74.0ms	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))
77.0ms	(sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5096	3356

prune134.0ms

Filtered

107 candidates to 144 candidates (-34.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	144	6	150

Merged error: 0b

Counts

150 → 6

regimes13.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms

sample2.0s

Algorithm

intervals

Results

842.0ms	1615×	body	2560	valid
475.0ms	1249×	body	1280	valid
265.0ms	1535×	body	640	valid
120.0ms	983×	body	320	valid
90.0ms	2205×	body	80	valid
40.0ms	413×	body	160	valid

Details

analyze244.0ms

sample56.0ms

simplify28.0ms

prune1.0ms

localize6.0ms

rewrite13.0ms

series43.0ms

simplify73.0ms

prune55.0ms

localize11.0ms

rewrite31.0ms

series138.0ms

simplify120.0ms

prune84.0ms

localize11.0ms

rewrite97.0ms

series198.0ms

simplify353.0ms

prune671.0ms

localize13.0ms

rewrite35.0ms

series334.0ms

simplify84.0ms

prune134.0ms

regimes13.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.0s

Profiling