Details

analyze533.0ms (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune5.0ms (0.2%)

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: 24.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
1.1b	(+.f64 (.f64 a c) (.f64 b d))
24.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 53

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series45.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
10.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify84.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5336	1420

prune74.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	53	9	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	9	63

Merged error: 23.9b

Counts

63 → 9

Compiler

Compiled 1631 to 318 computations (80.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 (.f64 a c) (.f64 b d))
14.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series65.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
11.0ms	(+.f64 (.f64 a c) (.f64 b d))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5505	2326

prune73.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 22.1b

Counts

105 → 10

Compiler

Compiled 3361 to 470 computations (86% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.5b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
1.1b	(+.f64 (.f64 a c) (.f64 b d))
23.9b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `times-frac_binary64`
17×	`add-exp-log_binary64`
15×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

14.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
7.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series54.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
12.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5039	2169

prune71.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	109	10	119

Merged error: 22.1b

Counts

119 → 10

Compiler

Compiled 2726 to 618 computations (77.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.7b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
1.1b	(+.f64 (.f64 a c) (.f64 b d))
23.8b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
56×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`flip3-+_binary64` `add-log-exp_binary64` `div-exp_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 137

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))
11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series67.0ms (2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
20.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))
10.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify124.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4993	4822
1	4993	4822

prune73.0ms (2.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	149	10	159

Merged error: 22.1b

Counts

159 → 10

Compiler

Compiled 4192 to 674 computations (83.9% saved)

regimes230.0ms (6.8%)

Compiler: Compiled 876 to 512 computations (41.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	38
1	18	38

end0.0ms (0%)

sample1.4s (43%)

Algorithm

1×

intervals

Results

356.0ms	8000×	body	80	valid
18.0ms	432×	body	80	invalid

Compiler

Compiled 294 to 169 computations (42.5% saved)

Details

analyze533.0ms (15.8%)

sample21.0ms (0.6%)

simplify12.0ms (0.4%)

prune5.0ms (0.2%)

localize13.0ms (0.4%)

rewrite20.0ms (0.6%)

series45.0ms (1.4%)

simplify84.0ms (2.5%)

prune74.0ms (2.2%)

localize13.0ms (0.4%)

rewrite27.0ms (0.8%)

series65.0ms (1.9%)

simplify108.0ms (3.2%)

prune73.0ms (2.2%)

localize11.0ms (0.3%)

rewrite33.0ms (1%)

series54.0ms (1.6%)

simplify111.0ms (3.3%)

prune71.0ms (2.1%)

localize11.0ms (0.3%)

rewrite37.0ms (1.1%)

series67.0ms (2%)

simplify124.0ms (3.7%)

prune73.0ms (2.2%)

regimes230.0ms (6.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (43%)

Profiling