Details

analyze1.3s (6.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4937	96
1	4937	96
0	3	3
1	3	3

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)

sample77.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	42×	body	2048	valid
15.0ms	165×	body	128	valid
10.0ms	19×	body	4096	valid
7.0ms	20×	body	1024	valid
2.0ms	26×	body	128	nan
2.0ms	6×	body	512	valid
1.0ms	10×	body	128	invalid
1.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify543.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (533.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune7.0ms (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

35.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite259.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

35.4b

Rules

17×	`add-sqr-sqrt_binary64_3510`
14×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
12×	`*-un-lft-identity_binary64_3488`
10×	`pow1_binary64_3549`
8×	`add-cube-cbrt_binary64_3523`
6×	`add-log-exp_binary64_3527` `times-frac_binary64_3494` `associate-/l*_binary64_3433`
5×	`sqrt-prod_binary64_3504`
4×	`prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `difference-of-squares_binary64_3457`
3×	`flip3--_binary64_3492` `flip--_binary64_3463` `pow-prod-down_binary64_3559` `associate-r_binary64_3428`
2×	`sqrt-div_binary64_3505` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `distribute-lft-out--_binary64_3440` `associate-/l/_binary64_3435`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `cancel-sign-sub-inv_binary64_3454` `frac-2neg_binary64_3499` `div-sub_binary64_3493` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/r_binary64_3432` `associate-l_binary64_3429` `-commutative_binary64_3419`

Counts

4 → 75

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(.f64 (.f64 3 a) c)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Compiler

Compiled 2006 to 1174 computations (41.5% saved)

series1.1s (6%)

Error

5.3b

Counts

4 → 60

Calls

4 calls:

364.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
264.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
261.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
86.0ms	(.f64 (.f64 3 a) c)

Compiler

Compiled 2706 to 2054 computations (24.1% saved)

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5371	2461

prune251.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

5.3b

Counts

136 → 10

Compiler

Compiled 2774 to 1538 computations (44.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (/.f64 1/3 a))
0.4b	(/.f64 1/3 a)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite255.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

31×	`add-sqr-sqrt_binary64_3510`
23×	`*-un-lft-identity_binary64_3488`
21×	`add-cube-cbrt_binary64_3523`
19×	`times-frac_binary64_3494`
13×	`associate-r_binary64_3428`
11×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
7×	`pow1_binary64_3549`
6×	`add-log-exp_binary64_3527` `associate-l_binary64_3429`
4×	`flip3--_binary64_3492` `flip--_binary64_3463` `sqrt-prod_binary64_3504`
3×	`associate-/l_binary64_3433` `associate-/r_binary64_3432`
2×	`sqrt-div_binary64_3505` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `unswap-sqr_binary64_3456` `associate-*l/_binary64_3431` `difference-of-squares_binary64_3457`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `cancel-sign-sub-inv_binary64_3454` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `pow-prod-down_binary64_3559` `associate-r/_binary64_3430` `distribute-lft-out--_binary64_3440` `-commutative_binary64_3419`

Counts

4 → 93

Calls

4 calls:

30.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (/.f64 1/3 a))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(/.f64 1/3 a)

Compiler

Compiled 2478 to 1464 computations (40.9% saved)

series994.0ms (5.5%)

Error

5.3b

Counts

4 → 57

Calls

4 calls:

362.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (/.f64 1/3 a))
276.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
246.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
27.0ms	(/.f64 1/3 a)

Compiler

Compiled 2562 to 1955 computations (23.7% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5020	2776

prune267.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	149	11	160

Error

5.3b

Counts

160 → 11

Compiler

Compiled 3173 to 1791 computations (43.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a)
0.4b	(/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a))
0.4b	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite850.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

156×	`times-frac_binary64_3494`
144×	`add-sqr-sqrt_binary64_3510`
111×	`*-un-lft-identity_binary64_3488`
79×	`add-cube-cbrt_binary64_3523`
32×	`difference-of-squares_binary64_3457`
25×	`associate-/r*_binary64_3432`
19×	`sqrt-prod_binary64_3504`
16×	`distribute-lft-out--_binary64_3440`
11×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
9×	`associate-/l*_binary64_3433`
6×	`add-log-exp_binary64_3527` `div-inv_binary64_3485`
5×	`pow1_binary64_3549`
4×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
3×	`flip3--_binary64_3492` `flip--_binary64_3463`
2×	`sqrt-div_binary64_3505` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `associate-/l/_binary64_3435`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `cancel-sign-sub-inv_binary64_3454` `associate-/r/_binary64_3434` `div-sub_binary64_3493`

Counts

4 → 175

Calls

4 calls:

22.0ms	(/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a))
20.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a)
8.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 6055 to 3355 computations (44.6% saved)

series1.5s (8.1%)

Error

5.3b

Counts

4 → 72

Calls

4 calls:

493.0ms	(/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a))
317.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b) a)
265.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
262.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 3684 to 2862 computations (22.3% saved)

simplify173.0ms (1%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5251	7764

prune609.0ms (3.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	246	12	258

Error

5.3b

Counts

258 → 12

Compiler

Compiled 6960 to 3902 computations (43.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a))
0.4b	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
8.4b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite271.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

15×	`*-un-lft-identity_binary64_3488`
14×	`add-sqr-sqrt_binary64_3510`
11×	`add-cube-cbrt_binary64_3523` `times-frac_binary64_3494`
9×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `sqrt-prod_binary64_3504`
8×	`add-log-exp_binary64_3527` `cancel-sign-sub-inv_binary64_3454`
6×	`associate-/l*_binary64_3433`
5×	`pow1_binary64_3549`
4×	`flip3--_binary64_3492` `sqrt-div_binary64_3505` `flip--_binary64_3463` `div-inv_binary64_3485`
2×	`diff-log_binary64_3580` `sub-neg_binary64_3481` `distribute-lft-out--_binary64_3440` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `associate-/l/_binary64_3435`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `frac-sub_binary64_3497` `sub-div_binary64_3495` `difference-of-squares_binary64_3457` `distribute-rgt-out--_binary64_3442` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `associate-/r*_binary64_3432`

Counts

4 → 80

Calls

4 calls:

26.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
21.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))

Compiler

Compiled 2581 to 1446 computations (44% saved)

series1.5s (8.3%)

Error

5.3b

Counts

4 → 73

Calls

4 calls:

421.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a)) (/.f64 b (*.f64 3 a)))
414.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))) (.f64 3 a))
282.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
270.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))

Compiler

Compiled 3913 to 2975 computations (24% saved)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5193	3200

prune282.0ms (1.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	153	12	165

Error

5.3b

Counts

165 → 12

Compiler

Compiled 3557 to 1994 computations (43.9% saved)

regimes2.6s (14.3%)

Accuracy

Total 5.3b remaining (47.6%)

Threshold costs 0b (0%)

Compiler

Compiled 8464 to 6716 computations (20.7% saved)

bsearch116.0ms (0.6%)

Steps

Iters	Range		Point
8	7.726734627321722e-138	5.832221787937052e-134	1.8586457953181464e-134
8	-5.222027993423419e+93	-4.0928987339401984e+89	-4.666147932669531e+93

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	108	59
1	108	59

end0.0ms (0%)

sample4.8s (26.5%)

Algorithm

1×

intervals

Results

507.0ms	1120×	body	2048	valid
464.0ms	5222×	body	128	valid
252.0ms	693×	body	1024	valid
212.0ms	393×	body	4096	valid
110.0ms	398×	body	512	valid
72.0ms	685×	body	128	nan
33.0ms	368×	body	128	invalid
30.0ms	174×	body	256	valid

Compiler

Compiled 1614 to 1282 computations (20.6% saved)

Details

analyze1.3s (6.9%)

sample77.0ms (0.4%)

simplify543.0ms (3%)

prune7.0ms (0%)

localize19.0ms (0.1%)

rewrite259.0ms (1.4%)

series1.1s (6%)

simplify96.0ms (0.5%)

prune251.0ms (1.4%)

localize22.0ms (0.1%)

rewrite255.0ms (1.4%)

series994.0ms (5.5%)

simplify136.0ms (0.8%)

prune267.0ms (1.5%)

localize24.0ms (0.1%)

rewrite850.0ms (4.7%)

series1.5s (8.1%)

simplify173.0ms (1%)

prune609.0ms (3.4%)

localize29.0ms (0.2%)

rewrite271.0ms (1.5%)

series1.5s (8.3%)

simplify106.0ms (0.6%)

prune282.0ms (1.6%)

regimes2.6s (14.3%)

bsearch116.0ms (0.6%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.8s (26.5%)

Profiling