Details

analyze610.0ms (10.2%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	188×	body	128	valid
6.0ms	27×	body	2048	valid
6.0ms	11×	body	4096	valid
3.0ms	20×	body	1024	valid
2.0ms	23×	body	128	nan
1.0ms	4×	body	512	valid
1.0ms	6×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify195.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 31.8b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series442.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
123.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4922	2470
1	4922	2470

prune114.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 4.9b

Counts

102 → 10

Compiler

Compiled 2303 to 469 computations (79.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
7×	`pow1_binary64` `associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`diff-log_binary64` `unswap-sqr_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate--l-_binary64` `1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

17.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series427.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
116.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5009	2096

prune88.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 4.9b

Counts

109 → 10

Compiler

Compiled 2235 to 624 computations (72.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite59.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series482.0ms (8%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
112.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
58.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5004	5825

prune165.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	187	10	197

Merged error: 4.8b

Counts

197 → 10

Compiler

Compiled 4904 to 969 computations (80.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0b	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
24.5b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
24.5b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`diff-log_binary64`
2×	`sub-neg_binary64` `pow1/3_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `neg-log_binary64`

Counts

4 → 50

Calls

4 calls:

5.0ms	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series592.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
164.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
151.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4866	1511
1	4866	1511

prune62.0ms (1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	62	10	72

Merged error: 4.8b

Counts

72 → 10

Compiler

Compiled 1928 to 400 computations (79.3% saved)

regimes624.0ms (10.4%)

Compiler: Compiled 2827 to 1761 computations (37.7% saved)

bsearch67.0ms (1.1%)

Steps

Iters	Range		Point
10	2.6984454119678255e-12	3.813352894740704	3.7738771228718737
9	-1.2594274734414935e-50	-3.252894960030989e-60	-2.179096873024578e-55

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	111	55
1	111	55

end0.0ms (0%)

sample1.6s (26.1%)

Algorithm

1×

intervals

Results

247.0ms	1174×	body	2048	valid
232.0ms	5161×	body	128	valid
134.0ms	721×	body	1024	valid
94.0ms	358×	body	4096	valid
47.0ms	388×	body	512	valid
33.0ms	777×	body	128	nan
16.0ms	198×	body	256	valid
11.0ms	260×	body	128	invalid

Compiler

Compiled 718 to 453 computations (36.9% saved)

Details

analyze610.0ms (10.2%)

sample38.0ms (0.6%)

simplify195.0ms (3.3%)

prune4.0ms (0.1%)

localize18.0ms (0.3%)

rewrite43.0ms (0.7%)

series442.0ms (7.4%)

simplify78.0ms (1.3%)

prune114.0ms (1.9%)

localize11.0ms (0.2%)

rewrite44.0ms (0.7%)

series427.0ms (7.1%)

simplify56.0ms (0.9%)

prune88.0ms (1.5%)

localize11.0ms (0.2%)

rewrite59.0ms (1%)

series482.0ms (8%)

simplify92.0ms (1.5%)

prune165.0ms (2.7%)

localize13.0ms (0.2%)

rewrite23.0ms (0.4%)

series592.0ms (9.9%)

simplify73.0ms (1.2%)

prune62.0ms (1%)

regimes624.0ms (10.4%)

bsearch67.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (26.1%)

Profiling