Details

analyze691.0ms (14.8%)

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)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify199.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	514	22
1	514	22

prune3.0ms (0.1%)

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: 24.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(-.f64 (.f64 b c) (.f64 a d))
24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
9×	`times-frac_binary64_2442`
7×	`add-log-exp_binary64_2472`
5×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
3×	`associate-/l_binary64_2383` `associate-/r_binary64_2382` `pow1_binary64_2494`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `flip3--_binary64_2440` `associate-/l/_binary64_2385` `flip--_binary64_2411`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `div-sub_binary64_2441` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

3 → 54

Calls

3 calls:

10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series321.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

201.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
82.0ms	(-.f64 (.f64 b c) (.f64 a d))
38.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6056	1456

prune86.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 24.0b

Counts

64 → 10

Compiler

Compiled 1721 to 335 computations (80.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b c) (.f64 a d))
18.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2457`
21×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
18×	`sqrt-prod_binary64_2451` `times-frac_binary64_2442`
6×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `associate-/r*_binary64_2382` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494` `sqrt-div_binary64_2452`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384` `pow1/2_binary64_2513` `flip3--_binary64_2440` `rem-sqrt-square_binary64_2449` `associate-/l/_binary64_2385` `flip--_binary64_2411` `sqrt-pow1_binary64_2453`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `clear-num_binary64_2435` `div-sub_binary64_2441` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
6.0ms	(-.f64 (.f64 b c) (.f64 a d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series440.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
83.0ms	(-.f64 (.f64 b c) (.f64 a d))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
48.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4913	2368
1	4913	2368

prune109.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 21.8b

Counts

107 → 11

Compiler

Compiled 3444 to 510 computations (85.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 c b) (.f64 d a))
18.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2457`
21×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
18×	`sqrt-prod_binary64_2451` `times-frac_binary64_2442`
6×	`associate-/l*_binary64_2383` `add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494` `sqrt-div_binary64_2452`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r*_binary64_2382`
2×	`associate-/r/_binary64_2384` `pow1/2_binary64_2513` `flip3--_binary64_2440` `rem-sqrt-square_binary64_2449` `associate-/l/_binary64_2385` `flip--_binary64_2411` `sqrt-pow1_binary64_2453`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

4 → 84

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 c b) (.f64 d a))

series326.0ms (7%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
80.0ms	(-.f64 (.f64 c b) (.f64 d a))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
41.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4988	2352
1	4988	2352

prune108.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 21.8b

Counts

107 → 11

Compiler

Compiled 3593 to 695 computations (80.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
18.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite78.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2457`
76×	`times-frac_binary64_2442`
53×	`*-un-lft-identity_binary64_2436`
47×	`add-cube-cbrt_binary64_2468` `sqrt-prod_binary64_2451`
28×	`add-exp-log_binary64_2471`
24×	`associate-r_binary64_2378` `associate-l_binary64_2379`
18×	`add-cbrt-cube_binary64_2469`
15×	`unswap-sqr_binary64_2404`
10×	`sqrt-div_binary64_2452`
9×	`div-exp_binary64_2484`
8×	`prod-exp_binary64_2482` `pow1_binary64_2494`
6×	`associate-/r/_binary64_2384` `associate-/r*_binary64_2382`
5×	`flip3-+_binary64_2439` `cbrt-undiv_binary64_2467` `flip-+_binary64_2410`
4×	`add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466`
3×	`div-inv_binary64_2433` `associate-/l*_binary64_2383`
2×	`rec-exp_binary64_2483` `1-exp_binary64_2477` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `associate-/l/_binary64_2385` `sqrt-pow1_binary64_2453`
1×	`-commutative_binary64_2369` `pow-prod-down_binary64_2504` `flip3--_binary64_2440` `associate-r/_binary64_2380` `clear-num_binary64_2435` `div-sub_binary64_2441` `frac-2neg_binary64_2447` `associate-*l/_binary64_2381` `frac-times_binary64_2446` `flip--_binary64_2411`

Counts

4 → 161

Calls

4 calls:

31.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a 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)))

series622.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
257.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
44.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
42.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5418	5575

prune161.0ms (3.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	171	13	184

Merged error: 21.8b

Counts

184 → 13

Compiler

Compiled 6076 to 814 computations (86.6% saved)

regimes150.0ms (3.2%)

Compiler: Compiled 1412 to 920 computations (34.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	83
1	51	83

end0.0ms (0%)

sample898.0ms (19.2%)

Algorithm

1×

intervals

Results

365.0ms	8000×	body	128	valid
21.0ms	479×	body	128	invalid

Compiler

Compiled 373 to 222 computations (40.5% saved)

Details

analyze691.0ms (14.8%)

sample23.0ms (0.5%)

simplify199.0ms (4.3%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

rewrite23.0ms (0.5%)

series321.0ms (6.9%)

simplify66.0ms (1.4%)

prune86.0ms (1.8%)

localize13.0ms (0.3%)

rewrite35.0ms (0.8%)

series440.0ms (9.4%)

simplify85.0ms (1.8%)

prune109.0ms (2.3%)

localize15.0ms (0.3%)

rewrite38.0ms (0.8%)

series326.0ms (7%)

simplify62.0ms (1.3%)

prune108.0ms (2.3%)

localize14.0ms (0.3%)

rewrite78.0ms (1.7%)

series622.0ms (13.3%)

simplify91.0ms (1.9%)

prune161.0ms (3.5%)

regimes150.0ms (3.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample898.0ms (19.2%)

Profiling