Details

analyze540.0ms (17.7%)

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

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	8×	body	80	invalid

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune7.0ms (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: 29.7b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
29.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite29.0ms (1%)

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:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(+.f64 (.f64 c c) (.f64 d d))
8.0ms	(+.f64 (.f64 a c) (.f64 b d))

series61.0ms (2%)

Counts

3 → 9

Calls

3 calls:

41.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
13.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify49.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5334	951

prune106.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 28.9b

Counts

63 → 9

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
19.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite25.0ms (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:

10.0ms	(/.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)))

series69.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.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)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5503	1525

prune132.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 24.9b

Counts

105 → 11

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b))))
19.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b)))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite41.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
27×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
9×	`associate-/l*_binary64`
8×	`flip3-+_binary64` `div-exp_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`div-inv_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 193

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series78.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b))))
29.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (+.f64 (.f64 c a) (.f64 d b)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify74.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	4856
1	4962	4856

prune223.0ms (7.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	205	11	216

Merged error: 24.9b

Counts

216 → 11

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
19.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite55.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
18×	`add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64`
10×	`sqrt-div_binary64`
9×	`div-exp_binary64`
8×	`pow1_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

27.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series92.0ms (3%)

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))))
36.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify68.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4989	3794
1	4989	3794

prune161.0ms (5.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	171	12	183

Merged error: 24.9b

Counts

183 → 12

regimes492.0ms (16.1%)

Accuracy

Total 2.2b remaining (8.6%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	83
1	29	83

end0.0ms (0%)

sample601.0ms (19.7%)

Algorithm

1×

intervals

Results

365.0ms	8000×	body	80	valid
22.0ms	496×	body	80	invalid

Details

analyze540.0ms (17.7%)

sample24.0ms (0.8%)

simplify5.0ms (0.2%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite29.0ms (1%)

series61.0ms (2%)

simplify49.0ms (1.6%)

prune106.0ms (3.5%)

localize12.0ms (0.4%)

rewrite25.0ms (0.8%)

series69.0ms (2.3%)

simplify62.0ms (2%)

prune132.0ms (4.3%)

localize13.0ms (0.4%)

rewrite41.0ms (1.4%)

series78.0ms (2.5%)

simplify74.0ms (2.4%)

prune223.0ms (7.3%)

localize14.0ms (0.4%)

rewrite55.0ms (1.8%)

series92.0ms (3%)

simplify68.0ms (2.2%)

prune161.0ms (5.3%)

regimes492.0ms (16.1%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample601.0ms (19.7%)

Profiling