Details

analyze132.0ms (1.9%)

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)

sample24.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify147.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5029	46

prune3.0ms (0%)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize16.0ms (0.2%)

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

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_2503` `pow1_binary64_2526`
14×	`add-cbrt-cube_binary64_2501`
10×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
8×	`add-cube-cbrt_binary64_2500`
7×	`associate-r_binary64_2405`
6×	`add-log-exp_binary64_2504` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
4×	`distribute-lft-in_binary64_2414` `associate-*r/_binary64_2407` `distribute-rgt-in_binary64_2415`
3×	`unpow-prod-down_binary64_2544` `pow-unpow_binary64_2542`
2×	`flip3-+_binary64_2468` `-commutative_binary64_2396` `flip-+_binary64_2439` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `cancel-sign-sub-inv_binary64_2431` `associate-+r+_binary64_2397` `associate-l*_binary64_2406`
1×	`+-commutative_binary64_2395` `unpow2_binary64_2530` `flip--_binary64_2440` `sum-log_binary64_2556` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `sqr-pow_binary64_2437` `pow-pow_binary64_2537` `distribute-lft-out_binary64_2416` `flip3--_binary64_2469`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+.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))))))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series172.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(+.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))))))
35.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
31.0ms	(.f64 (.f64 a a) (+.f64 1 a))
28.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5227	1848

prune141.0ms (2%)

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

Error

0.0b

Counts

93 → 2

Compiler

Compiled 3498 to 1883 computations (46.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.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))))))
0.0b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.7b	(.f64 (.f64 a a) (*.f64 b b))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_2526`
32×	`associate-*r/_binary64_2407`
26×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
20×	`pow-prod-down_binary64_2536` `frac-add_binary64_2473`
14×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
13×	`add-log-exp_binary64_2504`
8×	`-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487` `associate-r*_binary64_2405`
6×	`sum-log_binary64_2556` `add-cube-cbrt_binary64_2500`
5×	`flip--_binary64_2440` `flip3--_binary64_2469`
4×	`distribute-lft-in_binary64_2414` `pow-plus_binary64_2528` `distribute-rgt-in_binary64_2415` `pow-prod-up_binary64_2535`
3×	`-commutative_binary64_2396` `unswap-sqr_binary64_2433` `associate-l*_binary64_2406`
2×	`sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `pow2_binary64_2546` `associate-+r+_binary64_2397` `pow-sqr_binary64_2438`
1×	`+-commutative_binary64_2395` `associate-+l+_binary64_2398` `distribute-lft-out_binary64_2416`

Counts

4 → 106

Calls

4 calls:

29.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.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))))))
9.0ms	(.f64 (.f64 a a) (*.f64 b b))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series174.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.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))))))
33.0ms	(.f64 (.f64 a a) (+.f64 1 a))
31.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
26.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5069	4771

prune318.0ms (4.6%)

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

Error

Counts

120 → 2

Compiler

Compiled 6546 to 3973 computations (39.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64_2407`
20×	`frac-add_binary64_2473`
17×	`add-exp-log_binary64_2503` `pow1_binary64_2526`
14×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-cbrt-cube_binary64_2501`
13×	`add-log-exp_binary64_2504`
9×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
7×	`add-cube-cbrt_binary64_2500` `prod-exp_binary64_2514` `associate-r_binary64_2405` `pow-prod-down_binary64_2536`
6×	`sum-log_binary64_2556` `cbrt-unprod_binary64_2498`
5×	`flip--_binary64_2440` `flip3--_binary64_2469`
4×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
3×	`pow-unpow_binary64_2542`
2×	`-commutative_binary64_2396` `pow-exp_binary64_2533` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `cancel-sign-sub-inv_binary64_2431` `pow-pow_binary64_2537` `associate-+r+_binary64_2397` `associate-l*_binary64_2406`
1×	`+-commutative_binary64_2395` `unpow2_binary64_2530` `associate-+l+_binary64_2398` `pow-to-exp_binary64_2534` `unpow-prod-down_binary64_2544` `sqr-pow_binary64_2437` `distribute-lft-out_binary64_2416`

Counts

4 → 95

Calls

4 calls:

19.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 a b) 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))))))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms	(pow.f64 (*.f64 a b) 2)

series163.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 a b) 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))))))
32.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
30.0ms	(.f64 (.f64 a a) (+.f64 1 a))
21.0ms	(pow.f64 (*.f64 a b) 2)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5285	4468

prune288.0ms (4.1%)

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

Error

Counts

109 → 2

Compiler

Compiled 5807 to 3857 computations (33.6% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
2.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
3.6b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
41.9b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

rewrite88.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
44×	`associate-+r+_binary64_2397`
33×	`*-un-lft-identity_binary64_2465`
32×	`cancel-sign-sub-inv_binary64_2431`
23×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
15×	`unpow-prod-down_binary64_2544`
12×	`times-frac_binary64_2471`
8×	`add-log-exp_binary64_2504` `associate--l+_binary64_2402`
7×	`add-exp-log_binary64_2503`
6×	`add-cbrt-cube_binary64_2501`
5×	`sqr-pow_binary64_2437` `pow1_binary64_2526` `distribute-lft-out_binary64_2416`
4×	`flip3-+_binary64_2468` `unpow2_binary64_2530` `flip-+_binary64_2439` `sub-neg_binary64_2458` `associate-/l*_binary64_2410`
3×	`associate-/r*_binary64_2409` `pow-unpow_binary64_2542`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `div-exp_binary64_2516` `div-inv_binary64_2462` `pow-pow_binary64_2537` `frac-2neg_binary64_2476`

Counts

4 → 119

Calls

4 calls:

21.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
17.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
11.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)

series2.6s (36.6%)

Counts

4 → 12

Calls

4 calls:

1.1s	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
700.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
521.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
180.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4997	12242
1	4997	12242

prune846.0ms (12.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	131	2	133

Error

Counts

133 → 2

Compiler

Compiled 15866 to 8275 computations (47.8% saved)

regimes198.0ms (2.8%)

Accuracy

Total 0.0b remaining (69%)

Threshold costs 0.0b (69%)

Compiler

Compiled 3251 to 2082 computations (36% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	80	55
1	80	55

end0.0ms (0%)

sample1.1s (15.9%)

Algorithm

1×

intervals

Results

538.0ms	8000×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 610 to 400 computations (34.4% saved)

Details

analyze132.0ms (1.9%)

sample24.0ms (0.3%)

simplify147.0ms (2.1%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite37.0ms (0.5%)

series172.0ms (2.5%)

simplify44.0ms (0.6%)

prune141.0ms (2%)

localize21.0ms (0.3%)

rewrite71.0ms (1%)

series174.0ms (2.5%)

simplify84.0ms (1.2%)

prune318.0ms (4.6%)

localize21.0ms (0.3%)

rewrite58.0ms (0.8%)

series163.0ms (2.3%)

simplify80.0ms (1.1%)

prune288.0ms (4.1%)

localize29.0ms (0.4%)

rewrite88.0ms (1.3%)

series2.6s (36.6%)

simplify154.0ms (2.2%)

prune846.0ms (12.1%)

regimes198.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (15.9%)

Profiling