Details

analyze521.0ms (13.9%)

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)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify224.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5230	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

Error

26.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (.f64 b c) (.f64 a d))
26.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
9×	`times-frac_binary64_2471`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`associate-/r_binary64_2409` `associate-/l_binary64_2410`
2×	`flip--_binary64_2440` `associate-/l/_binary64_2412` `pow1_binary64_2526` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

2 → 44

Calls

2 calls:

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

series145.0ms (3.9%)

Counts

2 → 6

Calls

2 calls:

104.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
41.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6253	1269

prune66.0ms (1.8%)

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

Error

25.9b

Counts

51 → 8

Compiler

Compiled 1366 to 264 computations (80.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b c) (.f64 a d))
17.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2487`
21×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
18×	`times-frac_binary64_2471` `sqrt-prod_binary64_2481`
6×	`add-log-exp_binary64_2504` `associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `sqrt-div_binary64_2482`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/l*_binary64_2410`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `associate-/l/_binary64_2412` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

4 → 86

Calls

4 calls:

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)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series229.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
46.0ms	(-.f64 (.f64 b c) (.f64 a d))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5136	2374

prune100.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Error

22.8b

Counts

106 → 10

Compiler

Compiled 3388 to 475 computations (86% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b c) (.f64 a d))
17.8b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
28.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_2487`
24×	`associate-r_binary64_2405`
22×	`*-un-lft-identity_binary64_2465` `times-frac_binary64_2471`
20×	`add-cube-cbrt_binary64_2500`
17×	`sqrt-prod_binary64_2481`
13×	`add-exp-log_binary64_2503`
9×	`add-cbrt-cube_binary64_2501`
8×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482`
5×	`unswap-sqr_binary64_2433`
4×	`prod-exp_binary64_2514`
3×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `flip3--_binary64_2469` `associate-l_binary64_2406`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `pow1/2_binary64_2545` `div-exp_binary64_2516` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `sqrt-pow1_binary64_2483` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `un-div-inv_binary64_2463` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `diff-log_binary64_2557` `pow-prod-down_binary64_2536` `1-exp_binary64_2509`

Counts

4 → 95

Calls

4 calls:

16.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (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)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series228.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
44.0ms	(-.f64 (.f64 b c) (.f64 a d))
29.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
22.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5100	2287

prune108.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	107	10	117

Error

22.8b

Counts

117 → 10

Compiler

Compiled 3734 to 715 computations (80.9% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
0.6b	(-.f64 (.f64 b c) (.f64 a d))
25.9b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_2487`
20×	`*-un-lft-identity_binary64_2465` `times-frac_binary64_2471`
19×	`add-cube-cbrt_binary64_2500`
16×	`add-exp-log_binary64_2503`
15×	`associate-r_binary64_2405`
10×	`add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526`
5×	`add-log-exp_binary64_2504`
4×	`div-exp_binary64_2516` `associate-/r/_binary64_2411` `prod-exp_binary64_2514`
3×	`associate-/r_binary64_2409` `flip--_binary64_2440` `unswap-sqr_binary64_2433` `flip3--_binary64_2469` `associate-/l_binary64_2410` `associate-l_binary64_2406`
2×	`flip3-+_binary64_2468` `associate-*l/_binary64_2408` `frac-times_binary64_2475` `flip-+_binary64_2439` `rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `1-exp_binary64_2509` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `associate-r/_binary64_2407` `clear-num_binary64_2464` `sub-neg_binary64_2458` `un-div-inv_binary64_2463` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536`

Counts

3 → 87

Calls

3 calls:

16.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series169.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
40.0ms	(-.f64 (.f64 b c) (.f64 a d))
26.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

simplify67.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5467	1988

prune74.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	96	10	106

Error

22.8b

Counts

106 → 10

Compiler

Compiled 2266 to 454 computations (80% saved)

regimes311.0ms (8.3%)

Accuracy

Total 2.7b remaining (10.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4187 to 2291 computations (45.3% saved)

bsearch2.0ms (0.1%)

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	56	82
1	56	82

end0.0ms (0%)

sample1.1s (29.7%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
20.0ms	443×	body	128	invalid

Compiler

Compiled 904 to 485 computations (46.3% saved)

Details

analyze521.0ms (13.9%)

sample22.0ms (0.6%)

simplify224.0ms (6%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite17.0ms (0.5%)

series145.0ms (3.9%)

simplify65.0ms (1.7%)

prune66.0ms (1.8%)

localize11.0ms (0.3%)

rewrite30.0ms (0.8%)

series229.0ms (6.1%)

simplify71.0ms (1.9%)

prune100.0ms (2.7%)

localize13.0ms (0.3%)

rewrite39.0ms (1%)

series228.0ms (6.1%)

simplify69.0ms (1.8%)

prune108.0ms (2.9%)

localize10.0ms (0.3%)

rewrite33.0ms (0.9%)

series169.0ms (4.5%)

simplify67.0ms (1.8%)

prune74.0ms (2%)

regimes311.0ms (8.3%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.7%)

Profiling