Details

analyze1.0s (13%)

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)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify349.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	514	22
1	514	22

prune5.0ms (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: 26.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
1.2b	(-.f64 (.f64 b c) (.f64 a d))
26.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite53.0ms (0.7%)

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:

25.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(+.f64 (.f64 c c) (.f64 d d))
9.0ms	(-.f64 (.f64 b c) (.f64 a d))

series578.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

345.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
162.0ms	(-.f64 (.f64 b c) (.f64 a d))
71.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify121.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	6056	1456

prune161.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	12	64

Merged error: 26.1b

Counts

64 → 12

Compiler

Compiled 1724 to 353 computations (79.5% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b c) (.f64 a d))
16.5b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite61.0ms (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:

19.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(-.f64 (.f64 b c) (.f64 a d))

series806.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

487.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
150.0ms	(-.f64 (.f64 b c) (.f64 a d))
85.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
83.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify160.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4913	2368
1	4913	2368

prune204.0ms (2.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	4	6	10
Picked	0	1	1
Done	1	0	1
Total	95	14	109

Merged error: 23.4b

Counts

109 → 14

Compiler

Compiled 3501 to 544 computations (84.5% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 c b) (.f64 d a))
16.6b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite68.0ms (0.9%)

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:

21.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
9.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(-.f64 (.f64 c b) (.f64 d a))

series624.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

291.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
151.0ms	(-.f64 (.f64 c b) (.f64 d a))
96.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
85.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify113.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4988	2352
1	4988	2352

prune209.0ms (2.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	96	14	110

Merged error: 23.4b

Counts

110 → 14

Compiler

Compiled 3650 to 729 computations (80% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b c) (.f64 a d))
16.6b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite89.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_2457`
24×	`associate-r_binary64_2378`
22×	`*-un-lft-identity_binary64_2436` `times-frac_binary64_2442`
20×	`add-cube-cbrt_binary64_2468`
17×	`sqrt-prod_binary64_2451`
13×	`add-exp-log_binary64_2471`
9×	`add-cbrt-cube_binary64_2469`
8×	`pow1_binary64_2494`
6×	`add-log-exp_binary64_2472` `sqrt-div_binary64_2452`
5×	`unswap-sqr_binary64_2404`
4×	`prod-exp_binary64_2482`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `flip3--_binary64_2440` `associate-l_binary64_2379` `flip--_binary64_2411`
2×	`associate-/r/_binary64_2384` `pow1/2_binary64_2513` `div-exp_binary64_2484` `cbrt-unprod_binary64_2466` `rem-sqrt-square_binary64_2449` `associate-*l/_binary64_2381` `frac-times_binary64_2446` `sqrt-pow1_binary64_2453`
1×	`cbrt-undiv_binary64_2467` `un-div-inv_binary64_2434` `-commutative_binary64_2369` `div-inv_binary64_2433` `rec-exp_binary64_2483` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `1-exp_binary64_2477` `associate-r/_binary64_2380` `sub-neg_binary64_2429`

Counts

4 → 94

Calls

4 calls:

38.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(-.f64 (.f64 b c) (.f64 a d))

series769.0ms (10%)

Counts

4 → 12

Calls

4 calls:

433.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
149.0ms	(-.f64 (.f64 b c) (.f64 a d))
97.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
90.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5170	2281

prune185.0ms (2.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	106	14	120

Merged error: 23.4b

Counts

120 → 14

Compiler

Compiled 3575 to 619 computations (82.7% saved)

regimes223.0ms (2.9%)

Compiler: Compiled 1296 to 788 computations (39.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms (0%)

sample1.6s (21.4%)

Algorithm

1×

intervals

Results

642.0ms	8000×	body	128	valid
38.0ms	481×	body	128	invalid

Compiler

Compiled 400 to 239 computations (40.3% saved)

Details

analyze1.0s (13%)

sample42.0ms (0.5%)

simplify349.0ms (4.5%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite53.0ms (0.7%)

series578.0ms (7.5%)

simplify121.0ms (1.6%)

prune161.0ms (2.1%)

localize25.0ms (0.3%)

rewrite61.0ms (0.8%)

series806.0ms (10.5%)

simplify160.0ms (2.1%)

prune204.0ms (2.7%)

localize27.0ms (0.4%)

rewrite68.0ms (0.9%)

series624.0ms (8.1%)

simplify113.0ms (1.5%)

prune209.0ms (2.7%)

localize29.0ms (0.4%)

rewrite89.0ms (1.2%)

series769.0ms (10%)

simplify123.0ms (1.6%)

prune185.0ms (2.4%)

regimes223.0ms (2.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (21.4%)

Profiling