Details

analyze141.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify236.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4912	46
1	4912	46

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_2525` `pow1_binary64_2548`
14×	`add-cbrt-cube_binary64_2523`
10×	`*-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509`
8×	`add-cube-cbrt_binary64_2522`
7×	`associate-r_binary64_2427`
6×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `add-log-exp_binary64_2526`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `associate-*r/_binary64_2429`
3×	`pow-unpow_binary64_2564` `unpow-prod-down_binary64_2566`
2×	`unswap-sqr_binary64_2455` `sub-neg_binary64_2480` `-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `flip-+_binary64_2461` `flip3-+_binary64_2490` `associate-+r+_binary64_2419` `associate-l*_binary64_2428`
1×	`pow-exp_binary64_2555` `flip--_binary64_2462` `pow-to-exp_binary64_2556` `pow-pow_binary64_2559` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417` `sum-log_binary64_2578` `sqr-pow_binary64_2459` `unpow2_binary64_2552` `flip3--_binary64_2491`

Counts

4 → 80

Calls

4 calls:

10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series309.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
62.0ms	(.f64 (.f64 a a) (+.f64 1 a))
49.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5113	1848

prune210.0ms (4.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Merged error: 0.0b

Counts

93 → 2

Compiler

Compiled 4954 to 2829 computations (42.9% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.8b	(.f64 (.f64 b b) (*.f64 a a))

rewrite84.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_2548`
32×	`associate-*r/_binary64_2429`
26×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
20×	`pow-prod-down_binary64_2558` `frac-add_binary64_2495`
14×	`prod-exp_binary64_2536` `flip-+_binary64_2461` `flip3-+_binary64_2490` `cbrt-unprod_binary64_2520`
13×	`add-log-exp_binary64_2526`
8×	`-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509` `associate-r*_binary64_2427`
6×	`add-cube-cbrt_binary64_2522` `sum-log_binary64_2578`
5×	`flip--_binary64_2462` `flip3--_binary64_2491`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `pow-plus_binary64_2550` `pow-prod-up_binary64_2557`
3×	`unswap-sqr_binary64_2455` `-commutative_binary64_2418` `associate-l*_binary64_2428`
2×	`sub-neg_binary64_2480` `cancel-sign-sub-inv_binary64_2453` `pow-sqr_binary64_2460` `pow2_binary64_2568` `associate-+r+_binary64_2419`
1×	`associate-+l+_binary64_2420` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417`

Counts

4 → 106

Calls

4 calls:

34.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series305.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
66.0ms	(.f64 (.f64 a a) (+.f64 1 a))
63.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
43.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4936	4777
1	4936	4777

prune304.0ms (7.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	2	120

Merged error: 0.0b

Counts

120 → 2

Compiler

Compiled 6605 to 4026 computations (39% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(pow.f64 (*.f64 b a) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite67.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64_2429`
20×	`frac-add_binary64_2495`
17×	`add-exp-log_binary64_2525` `pow1_binary64_2548`
14×	`flip-+_binary64_2461` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523`
13×	`add-log-exp_binary64_2526`
9×	`*-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509`
7×	`prod-exp_binary64_2536` `add-cube-cbrt_binary64_2522` `pow-prod-down_binary64_2558` `associate-r_binary64_2427`
6×	`sum-log_binary64_2578` `cbrt-unprod_binary64_2520`
5×	`flip--_binary64_2462` `flip3--_binary64_2491`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436`
3×	`pow-unpow_binary64_2564`
2×	`pow-exp_binary64_2555` `unswap-sqr_binary64_2455` `sub-neg_binary64_2480` `-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `pow-pow_binary64_2559` `associate-+r+_binary64_2419` `associate-l*_binary64_2428`
1×	`associate-+l+_binary64_2420` `unpow-prod-down_binary64_2566` `pow-to-exp_binary64_2556` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417` `sqr-pow_binary64_2459` `unpow2_binary64_2552`

Counts

4 → 95

Calls

4 calls:

26.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms	(pow.f64 (*.f64 b a) 2)

series304.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
65.0ms	(.f64 (.f64 a a) (+.f64 1 a))
63.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
43.0ms	(pow.f64 (*.f64 b a) 2)

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5184	4474

prune297.0ms (6.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Merged error: 0.0b

Counts

109 → 2

Compiler

Compiled 5844 to 3899 computations (33.3% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
0.1b	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite68.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_2509`
30×	`*-un-lft-identity_binary64_2487`
18×	`times-frac_binary64_2493` `add-cube-cbrt_binary64_2522`
12×	`add-exp-log_binary64_2525`
11×	`add-cbrt-cube_binary64_2523`
10×	`pow1_binary64_2548`
8×	`difference-of-squares_binary64_2456`
6×	`associate-/r*_binary64_2431` `add-log-exp_binary64_2526`
4×	`distribute-lft-out--_binary64_2439`
3×	`distribute-rgt-in_binary64_2437` `pow-unpow_binary64_2564` `distribute-lft-in_binary64_2436` `unpow-prod-down_binary64_2566` `prod-exp_binary64_2536` `associate-/l_binary64_2432` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `associate-r*_binary64_2427`
2×	`flip--_binary64_2462` `sub-neg_binary64_2480` `cancel-sign-sub-inv_binary64_2453` `associate-/r/_binary64_2433` `flip-+_binary64_2461` `div-sub_binary64_2492` `flip3-+_binary64_2490` `associate-+r+_binary64_2419` `associate-/l/_binary64_2434` `associate-*r/_binary64_2429` `flip3--_binary64_2491`
1×	`pow-exp_binary64_2555` `unswap-sqr_binary64_2455` `-commutative_binary64_2418` `pow-to-exp_binary64_2556` `pow-pow_binary64_2559` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `unsub-neg_binary64_2481` `div-exp_binary64_2538` `sqr-pow_binary64_2459` `associate-l*_binary64_2428` `unpow2_binary64_2552` `associate-+r-_binary64_2421` `neg-sub0_binary64_2482` `cbrt-undiv_binary64_2521`

Counts

4 → 101

Calls

4 calls:

21.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
15.0ms	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series424.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
143.0ms	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
62.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
50.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5123	2857

prune220.0ms (5.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	113	2	115

Merged error: 0.0b

Counts

115 → 2

Compiler

Compiled 5003 to 2849 computations (43.1% saved)

regimes32.0ms (0.7%)

Compiler: Compiled 229 to 176 computations (23.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	55
1	78	55

end0.0ms (0%)

sample823.0ms (19.3%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 142 to 107 computations (24.6% saved)

Details

analyze141.0ms (3.3%)

sample25.0ms (0.6%)

simplify236.0ms (5.5%)

prune3.0ms (0.1%)

localize17.0ms (0.4%)

rewrite45.0ms (1.1%)

series309.0ms (7.2%)

simplify42.0ms (1%)

prune210.0ms (4.9%)

localize21.0ms (0.5%)

rewrite84.0ms (2%)

series305.0ms (7.1%)

simplify98.0ms (2.3%)

prune304.0ms (7.1%)

localize23.0ms (0.5%)

rewrite67.0ms (1.6%)

series304.0ms (7.1%)

simplify78.0ms (1.8%)

prune297.0ms (6.9%)

localize20.0ms (0.5%)

rewrite68.0ms (1.6%)

series424.0ms (9.9%)

simplify75.0ms (1.7%)

prune220.0ms (5.1%)

regimes32.0ms (0.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample823.0ms (19.3%)

Profiling