Details

analyze468.0ms (1%)

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%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

9.0ms	173×	body	128	valid
9.0ms	37×	body	2048	valid
5.0ms	23×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify365.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune3.0ms (0%)

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

Error

32.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_4874`
15×	`*-un-lft-identity_binary64_4852`
14×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888`
10×	`pow1_binary64_4913`
9×	`add-cube-cbrt_binary64_4887`
6×	`difference-of-squares_binary64_4821` `times-frac_binary64_4858` `associate-/l*_binary64_4797` `add-log-exp_binary64_4891` `sqrt-prod_binary64_4868`
4×	`cbrt-unprod_binary64_4885` `prod-exp_binary64_4901`
3×	`distribute-lft-out--_binary64_4804` `flip3--_binary64_4856` `cancel-sign-sub-inv_binary64_4818` `associate-r_binary64_4792` `flip--_binary64_4827` `pow-prod-down_binary64_4923`
2×	`associate-/l/_binary64_4799` `sqrt-div_binary64_4869` `cbrt-undiv_binary64_4886` `div-exp_binary64_4903`
1×	`associate-l_binary64_4793` `pow1/2_binary64_4932` `div-sub_binary64_4857` `sqrt-pow1_binary64_4870` `sub-neg_binary64_4845` `div-inv_binary64_4849` `rem-sqrt-square_binary64_4865` `clear-num_binary64_4851` `associate-/r_binary64_4796` `diff-log_binary64_4944` `frac-2neg_binary64_4863` `-commutative_binary64_4783`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series244.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
14.0ms	(.f64 (.f64 3 a) c)

simplify60.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5038	1907

prune140.0ms (0.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Error

5.1b

Counts

93 → 10

Compiler

Compiled 2292 to 1379 computations (39.8% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite101.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_4858`
440×	`add-sqr-sqrt_binary64_4874`
365×	`*-un-lft-identity_binary64_4852`
291×	`add-cube-cbrt_binary64_4887`
74×	`difference-of-squares_binary64_4821`
71×	`associate-/r*_binary64_4796`
40×	`sqrt-prod_binary64_4868`
37×	`distribute-lft-out--_binary64_4804`
30×	`add-exp-log_binary64_4890`
18×	`add-cbrt-cube_binary64_4888`
17×	`div-inv_binary64_4849`
15×	`div-exp_binary64_4903`
11×	`pow1_binary64_4913`
6×	`add-log-exp_binary64_4891` `cbrt-undiv_binary64_4886`
5×	`associate-/r/_binary64_4798`
3×	`1-exp_binary64_4896` `cbrt-unprod_binary64_4885` `cancel-sign-sub-inv_binary64_4818` `associate-/l_binary64_4797` `associate-r*_binary64_4792` `rec-exp_binary64_4902` `prod-exp_binary64_4901` `pow-prod-down_binary64_4923`
2×	`flip3--_binary64_4856` `sqrt-div_binary64_4869` `flip--_binary64_4827`
1×	`pow-flip_binary64_4926` `associate-l_binary64_4793` `pow1/2_binary64_4932` `sqrt-pow1_binary64_4870` `sub-neg_binary64_4845` `rem-sqrt-square_binary64_4865` `clear-num_binary64_4851` `inv-pow_binary64_4937` `diff-log_binary64_4944` `frac-2neg_binary64_4863` `*-commutative_binary64_4783`

Counts

4 → 362

Calls

4 calls:

27.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series250.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
14.0ms	(.f64 (.f64 3 a) c)

simplify188.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4986	16239
1	4986	16239

prune835.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	370	4	374
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	371	13	384

Error

5.1b

Counts

384 → 13

Compiler

Compiled 12982 to 7973 computations (38.6% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) (sqrt.f64 3)) (/.f64 (sqrt.f64 3) (/.f64 1 a)))
0.4b	(/.f64 (sqrt.f64 3) (/.f64 1 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite1.1s (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

11897×	`times-frac_binary64_4858`
6529×	`add-sqr-sqrt_binary64_4874`
5518×	`*-un-lft-identity_binary64_4852`
4508×	`add-cube-cbrt_binary64_4887`
3661×	`sqrt-prod_binary64_4868`
1010×	`difference-of-squares_binary64_4821`
505×	`distribute-lft-out--_binary64_4804`
380×	`div-inv_binary64_4849`
96×	`associate-/r*_binary64_4796`
48×	`add-exp-log_binary64_4890`
46×	`associate-/l*_binary64_4797`
43×	`associate-/r/_binary64_4798`
33×	`div-exp_binary64_4903`
30×	`add-cbrt-cube_binary64_4888`
18×	`cbrt-undiv_binary64_4886`
6×	`add-log-exp_binary64_4891`
5×	`pow1_binary64_4913`
3×	`1-exp_binary64_4896` `cancel-sign-sub-inv_binary64_4818` `rec-exp_binary64_4902`
2×	`flip3--_binary64_4856` `div-sub_binary64_4857` `clear-num_binary64_4851` `sqrt-div_binary64_4869` `flip--_binary64_4827` `frac-2neg_binary64_4863`
1×	`pow1/2_binary64_4932` `sqrt-pow1_binary64_4870` `associate-/l/_binary64_4799` `sub-neg_binary64_4845` `rem-sqrt-square_binary64_4865` `diff-log_binary64_4944`

Counts

4 → 3618

Calls

4 calls:

106.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) (sqrt.f64 3)) (/.f64 (sqrt.f64 3) (/.f64 1 a)))
10.0ms	(/.f64 (sqrt.f64 3) (/.f64 1 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series357.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) (sqrt.f64 3)) (/.f64 (sqrt.f64 3) (/.f64 1 a)))
71.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.0ms	(/.f64 (sqrt.f64 3) (/.f64 1 a))

simplify2.0s (4.1%)

Algorithm

1×	egg-herbie

Counts

3630 → 3630

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	5593	253932

prune37.8s (77.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	3625	5	3630
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	3628	15	3643

Error

5.0b

Counts

3643 → 15

Compiler

Compiled 165663 to 113605 computations (31.4% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.3b	(.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) 3) (/.f64 1 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite47.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_4874`
34×	`times-frac_binary64_4858` `*-un-lft-identity_binary64_4852`
31×	`add-exp-log_binary64_4890`
24×	`add-cube-cbrt_binary64_4887`
23×	`associate-l_binary64_4793`
21×	`add-cbrt-cube_binary64_4888`
16×	`associate-r_binary64_4792`
12×	`pow1_binary64_4913`
11×	`prod-exp_binary64_4901`
8×	`difference-of-squares_binary64_4821` `div-exp_binary64_4903`
7×	`cbrt-unprod_binary64_4885` `sqrt-prod_binary64_4868`
6×	`unswap-sqr_binary64_4820` `add-log-exp_binary64_4891`
4×	`distribute-lft-out--_binary64_4804` `cbrt-undiv_binary64_4886` `pow-prod-down_binary64_4923`
3×	`cancel-sign-sub-inv_binary64_4818`
2×	`flip3--_binary64_4856` `1-exp_binary64_4896` `div-inv_binary64_4849` `sqrt-div_binary64_4869` `rec-exp_binary64_4902` `flip--_binary64_4827` `*-commutative_binary64_4783`
1×	`pow1/2_binary64_4932` `frac-times_binary64_4862` `associate-r/_binary64_4794` `sqrt-pow1_binary64_4870` `sub-neg_binary64_4845` `rem-sqrt-square_binary64_4865` `associate-l/_binary64_4795` `diff-log_binary64_4944` `un-div-inv_binary64_4850`

Counts

4 → 116

Calls

4 calls:

19.0ms	(.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) 3) (/.f64 1 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series261.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) 3) (/.f64 1 a))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
15.0ms	(.f64 (.f64 3 a) c)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5288	2933

prune149.0ms (0.3%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	127	16	143

Error

5.0b

Counts

143 → 16

Compiler

Compiled 3174 to 1966 computations (38.1% saved)

regimes1.8s (3.6%)

Accuracy

Total 5.1b remaining (47.3%)

Threshold costs 0b (0%)

Compiler

Compiled 9760 to 7572 computations (22.4% saved)

bsearch61.0ms (0.1%)

Steps

Iters	Range		Point
7	0.001743911149778541	0.04777764753188632	0.009186349066712231
10	-2.2860812834988032e+125	-3.4779987925107406e+114	-8.014644714148473e+124

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	53
1	79	53

end0.0ms (0%)

sample2.6s (5.3%)

Algorithm

1×

intervals

Results

273.0ms	1101×	body	2048	valid
270.0ms	5180×	body	128	valid
143.0ms	722×	body	1024	valid
134.0ms	428×	body	4096	valid
58.0ms	386×	body	512	valid
33.0ms	673×	body	128	nan
18.0ms	362×	body	128	invalid
17.0ms	183×	body	256	valid

Compiler

Compiled 1861 to 1444 computations (22.4% saved)

Details

analyze468.0ms (1%)

sample38.0ms (0.1%)

simplify365.0ms (0.7%)

prune3.0ms (0%)

localize9.0ms (0%)

rewrite37.0ms (0.1%)

series244.0ms (0.5%)

simplify60.0ms (0.1%)

prune140.0ms (0.3%)

localize12.0ms (0%)

rewrite101.0ms (0.2%)

series250.0ms (0.5%)

simplify188.0ms (0.4%)

prune835.0ms (1.7%)

localize14.0ms (0%)

rewrite1.1s (2.2%)

series357.0ms (0.7%)

simplify2.0s (4.1%)

prune37.8s (77.1%)

localize11.0ms (0%)

rewrite47.0ms (0.1%)

series261.0ms (0.5%)

simplify72.0ms (0.1%)

prune149.0ms (0.3%)

regimes1.8s (3.6%)

bsearch61.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (5.3%)

Profiling