Details

analyze458.0ms (6.8%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	169×	body	128	valid
8.0ms	33×	body	2048	valid
6.0ms	19×	body	4096	valid
4.0ms	21×	body	1024	valid
2.0ms	10×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	16×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify229.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 34.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_772`
13×	`*-un-lft-identity_binary64_751`
9×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`add-log-exp_binary64_787`
7×	`add-cube-cbrt_binary64_783`
6×	`times-frac_binary64_757` `sqrt-prod_binary64_766` `associate-/l*_binary64_698` `difference-of-squares_binary64_720`
5×	`pow1_binary64_809`
4×	`flip--_binary64_726` `flip3--_binary64_755`
3×	`distribute-lft-out--_binary64_705`
2×	`associate-/l/_binary64_700` `sqrt-div_binary64_767` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sub-neg_binary64_744` `div-exp_binary64_799`
1×	`prod-exp_binary64_797` `div-sub_binary64_756` `rem-sqrt-square_binary64_764` `associate-/r*_binary64_697` `pow1/2_binary64_828` `div-inv_binary64_748` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `sqrt-pow1_binary64_768`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series525.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune120.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.5b

Counts

83 → 10

Compiler

Compiled 2131 to 1289 computations (39.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.9b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.2b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
22×	`times-frac_binary64_757`
21×	`*-un-lft-identity_binary64_751`
17×	`cbrt-undiv_binary64_782` `div-exp_binary64_799`
13×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
12×	`add-sqr-sqrt_binary64_772`
11×	`add-cube-cbrt_binary64_783` `associate-/l*_binary64_698`
6×	`add-log-exp_binary64_787` `associate-/r/_binary64_699`
5×	`distribute-lft-out_binary64_704` `associate-/r*_binary64_697` `pow1_binary64_809`
4×	`flip3-+_binary64_754` `div-inv_binary64_748` `flip-+_binary64_725`
3×	`sqrt-prod_binary64_766`
2×	`sqrt-div_binary64_767` `frac-2neg_binary64_762` `clear-num_binary64_750`
1×	`+-commutative_binary64_683` `associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `sum-log_binary64_839` `sqrt-pow1_binary64_768` `flip3--_binary64_755`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series950.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
304.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
137.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4940	3121
1	4940	3121

prune154.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	113	11	124

Merged error: 6.4b

Counts

124 → 11

Compiler

Compiled 3389 to 2094 computations (38.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.9b	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 a 2))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
16×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
14×	`cbrt-undiv_binary64_782` `div-exp_binary64_799`
12×	`*-un-lft-identity_binary64_751`
11×	`add-sqr-sqrt_binary64_772`
10×	`associate-r_binary64_693`
8×	`add-cube-cbrt_binary64_783`
7×	`pow1_binary64_809`
6×	`add-log-exp_binary64_787`
5×	`times-frac_binary64_757`
3×	`associate-l_binary64_694` `sqrt-prod_binary64_766`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `sqrt-div_binary64_767` `associate-/r/_binary64_699` `div-inv_binary64_748` `associate-*r/_binary64_695` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `unswap-sqr_binary64_719` `associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `associate-/r_binary64_697` `pow1/2_binary64_828` `flip--_binary64_726` `pow-prod-down_binary64_819` `-commutative_binary64_684` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-/l*_binary64_698` `sqrt-pow1_binary64_768` `flip3--_binary64_755`

Counts

4 → 87

Calls

4 calls:

17.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
15.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 a 2))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series931.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
296.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 a 2))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5001	2377

prune123.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	99	11	110

Merged error: 6.4b

Counts

110 → 11

Compiler

Compiled 2783 to 1728 computations (37.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.9b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
28×	`cbrt-undiv_binary64_782` `div-exp_binary64_799`
23×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
8×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
6×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `add-log-exp_binary64_787` `sqrt-prod_binary64_766`
4×	`sqrt-div_binary64_767`
3×	`associate-/l/_binary64_700`
2×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `sqrt-pow1_binary64_768` `flip3--_binary64_755`
1×	`frac-times_binary64_761` `distribute-lft-out_binary64_704` `+-commutative_binary64_683` `flip3-+_binary64_754` `associate-/r_binary64_697` `times-frac_binary64_757` `div-inv_binary64_748` `associate-r/_binary64_695` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-l/_binary64_696` `associate-/l_binary64_698` `flip-+_binary64_725`

Counts

4 → 86

Calls

4 calls:

28.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series708.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 c -4) (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (*.f64 a 2))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4992	3300
1	4992	3300

prune161.0ms (2.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	98	11	109

Merged error: 6.4b

Counts

109 → 11

Compiler

Compiled 3881 to 2371 computations (38.9% saved)

regimes171.0ms (2.5%)

Compiler: Compiled 735 to 573 computations (22% saved)

bsearch109.0ms (1.6%)

Steps

Iters	Range		Point
9	1.83876784517695e-41	3.3135969055397036e-33	2.3661654222815367e-37
9	7.173100178855411e-308	9.105006293718139e-300	7.29005784145621e-308
11	-2.4117062075701287e+73	-1.126996582450745e+52	-6.938492923479257e+71

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	91
1	108	91

end0.0ms (0%)

sample1.5s (21.6%)

Algorithm

1×

intervals

Results

275.0ms	1127×	body	2048	valid
274.0ms	5193×	body	128	valid
142.0ms	708×	body	1024	valid
124.0ms	407×	body	4096	valid
56.0ms	372×	body	512	valid
33.0ms	628×	body	128	nan
20.0ms	386×	body	128	invalid
18.0ms	193×	body	256	valid

Compiler

Compiled 364 to 270 computations (25.8% saved)

Details

analyze458.0ms (6.8%)

sample42.0ms (0.6%)

simplify229.0ms (3.4%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series525.0ms (7.8%)

simplify98.0ms (1.5%)

prune120.0ms (1.8%)

localize14.0ms (0.2%)

rewrite55.0ms (0.8%)

series950.0ms (14.1%)

simplify86.0ms (1.3%)

prune154.0ms (2.3%)

localize15.0ms (0.2%)

rewrite54.0ms (0.8%)

series931.0ms (13.8%)

simplify63.0ms (0.9%)

prune123.0ms (1.8%)

localize22.0ms (0.3%)

rewrite60.0ms (0.9%)

series708.0ms (10.5%)

simplify73.0ms (1.1%)

prune161.0ms (2.4%)

regimes171.0ms (2.5%)

bsearch109.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (21.6%)

Profiling