Details

analyze603.0ms (0.4%)

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)

sample42.0ms (0%)

Algorithm

1×

intervals

Results

11.0ms	163×	body	128	valid
8.0ms	39×	body	2048	valid
4.0ms	25×	body	1024	valid
3.0ms	12×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	23×	body	128	nan
0.0ms	7×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify169.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms (0%)

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

Error

35.2b

Counts

2 → 2

Compiler

Compiled 12 to 9 computations (25% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

8 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

series587.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

180.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
147.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
142.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
118.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1848 to 1494 computations (19.2% saved)

simplify60.0ms (0%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5260	3170

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.4b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.1b	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_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` `+-commutative_binary64`

Counts

4 → 80

Calls

8 calls:

11.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

series584.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

179.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
143.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
139.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
123.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1903 to 1549 computations (18.6% saved)

simplify53.0ms (0%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5169	2891

prune1.4s (0.9%)

Pruning

111 alts after pruning (109 fresh and 2 done)

	Pruned	Kept	Total
New	201	109	310
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	201	111	312

Error

5.7b

Counts

312 → 111

Compiler

Compiled 5431 to 2143 computations (60.5% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

7.6b	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
3.2b	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.2b	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
7.6b	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
13×	`sqrt-prod_binary64`
10×	`associate-/r*_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`diff-log_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 141

Calls

8 calls:

15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
15.0ms	(/.f64 (.f64 a c) (-.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))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series811.0ms (0.5%)

Counts

4 → 71

Calls

4 calls:

272.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
246.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
151.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
141.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2593 to 1897 computations (26.8% saved)

simplify104.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5505	5702

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

6.4b	(/.f64 (-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3)))) a)
3.9b	(/.f64 c (/.f64 b_2 a))
0.2b	(.f64 (.f64 a c) (*.f64 a c))
0.0b	(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)
3.9b	(/.f64 c (/.f64 b_2 a))
6.4b	(/.f64 (-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3)))) a)
9.1b	(-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))))
16.4b	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))

rewrite63.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64`
29×	`add-cbrt-cube_binary64`
28×	`associate-/r*_binary64`
24×	`prod-exp_binary64`
19×	`div-exp_binary64`
9×	`cbrt-undiv_binary64`
8×	`cbrt-unprod_binary64`
7×	`associate-/l*_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow-to-exp_binary64` `pow-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `associate-r/_binary64` `sqr-pow_binary64` `flip--_binary64` `frac-sub_binary64` `unpow3_binary64` `associate-l/_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64`

Counts

4 → 169

Calls

8 calls:

14.0ms	(-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))))
13.0ms	(/.f64 (-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3)))) a)
11.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))
6.0ms	(/.f64 c (/.f64 b_2 a))
0.0ms	(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)

series1.3s (0.9%)

Counts

4 → 54

Calls

4 calls:

567.0ms	(/.f64 (-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3)))) a)
439.0ms	(-.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 1/8 (/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))))
216.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b_2 3))
106.0ms	(/.f64 c (/.f64 b_2 a))

Compiler

Compiled 1770 to 1441 computations (18.6% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5047	5073

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.2b	(pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.2b	(pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3)
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
19.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite57.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
50×	`cbrt-prod_binary64`
48×	`add-cube-cbrt_binary64`
44×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`difference-of-squares_binary64`
16×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64` `cancel-sign-sub-inv_binary64`
2×	`flip3--_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `sub-neg_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`

Counts

4 → 156

Calls

8 calls:

12.0ms	(pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

series829.0ms (0.5%)

Counts

4 → 68

Calls

4 calls:

335.0ms	(pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3)
191.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3))
176.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2521 to 2089 computations (17.1% saved)

simplify115.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4988	6133
1	4988	6133

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)
0.2b	(.f64 b_2 (+.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) b_2))
15.4b	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.5b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3)) (.f64 a (-.f64 (.f64 b_2 (+.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) b_2)) (*.f64 a c))))

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
72×	`difference-of-squares_binary64`
57×	`unpow-prod-down_binary64` `cube-prod_binary64`
41×	`*-un-lft-identity_binary64`
33×	`associate-/l*_binary64` `times-frac_binary64`
31×	`sqr-pow_binary64`
30×	`sqrt-prod_binary64`
15×	`distribute-lft-out--_binary64`
12×	`cancel-sign-sub-inv_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`sqrt-div_binary64`
3×	`difference-cubes_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 169

Calls

8 calls:

43.0ms	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3)) (.f64 a (-.f64 (.f64 b_2 (+.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) b_2)) (*.f64 a c))))
21.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(.f64 b_2 (+.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) b_2))

series872.0ms (0.6%)

Counts

4 → 64

Calls

4 calls:

387.0ms	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3)) (.f64 a (-.f64 (.f64 b_2 (+.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) b_2)) (*.f64 a c))))
241.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
135.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3773 to 2585 computations (31.5% saved)

simplify108.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5131	8873

prune13.5s (8.8%)

Pruning

463 alts after pruning (457 fresh and 6 done)

	Pruned	Kept	Total
New	531	361	892
Fresh	8	96	104
Picked	0	0	0
Done	1	6	7
Total	540	463	1003

Error

5.7b

Counts

1003 → 463

Compiler

Compiled 30066 to 12545 computations (58.3% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.1b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

8 calls:

11.0ms	(/.f64 c (-.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))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))

series672.0ms (0.4%)

Counts

4 → 73

Calls

4 calls:

248.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
160.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
125.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2247 to 1838 computations (18.2% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5042	3495

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)
0.1b	(/.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
23.0b	(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))
24.4b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64`
27×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
6×	`difference-of-squares_binary64`
5×	`pow1_binary64` `rem-sqrt-square_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `sqr-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cube-div_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`pow1/2_binary64` `rem-cbrt-cube_binary64` `distribute-lft-out--_binary64`

Counts

4 → 88

Calls

8 calls:

14.0ms	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
7.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))
5.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2) a)

series532.0ms (0.3%)

Counts

4 → 73

Calls

4 calls:

144.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))
141.0ms	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
129.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
119.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))

Compiler

Compiled 1764 to 1451 computations (17.7% saved)

simplify70.0ms (0%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4995	2656
1	4995	2656

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.1b	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)
23.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
23.8b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.8b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.8b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64`
30×	`flip3--_binary64` `flip--_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
24×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
14×	`associate-*l/_binary64`
12×	`pow1/3_binary64`
9×	`pow-prod-up_binary64` `cbrt-prod_binary64`
8×	`associate-*r/_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`pow-plus_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-sqr_binary64`
2×	`pow2_binary64`
1×	`pow1/2_binary64` `pow3_binary64` `sqrt-prod_binary64`

Counts

4 → 89

Calls

8 calls:

22.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.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)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)

series856.0ms (0.6%)

Counts

4 → 71

Calls

4 calls:

238.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
235.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
224.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
159.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))

Compiler

Compiled 4516 to 2997 computations (33.6% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4965	4550
1	4965	4550

localize33.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(-.f64 (.f64 b_2 (+.f64 (+.f64 b_2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (sqrt.f64 (+.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2)) (*.f64 a c))
0.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)
0.1b	(.f64 b_2 (+.f64 (+.f64 b_2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (sqrt.f64 (+.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2))
15.4b	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
17.6b	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (sqrt.f64 (+.f64 (.f64 b_2 b_2) (*.f64 a c))))
18.3b	(sqrt.f64 (+.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite81.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64`
86×	`sqrt-prod_binary64`
54×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
45×	`difference-of-squares_binary64`
43×	`add-cube-cbrt_binary64`
28×	`unpow-prod-down_binary64`
21×	`cube-prod_binary64`
18×	`sqr-pow_binary64`
12×	`cancel-sign-sub-inv_binary64`
9×	`associate-/l*_binary64`
8×	`sqrt-div_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`distribute-lft-out--_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`difference-cubes_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 169

Calls

8 calls:

22.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
13.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(.f64 b_2 (+.f64 (+.f64 b_2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (sqrt.f64 (+.f64 (.f64 b_2 b_2) (.f64 a c))))) b_2))

series572.0ms (0.4%)

Counts

4 → 56

Calls

4 calls:

181.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3) (pow.f64 b_2 3))
164.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c)))) (sqrt.f64 (+.f64 (.f64 b_2 b_2) (*.f64 a c))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
95.0ms	(sqrt.f64 (+.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 4560 to 2822 computations (38.1% saved)

simplify136.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5003	6914

prune22.7s (14.7%)

Pruning

667 alts after pruning (656 fresh and 11 done)

	Pruned	Kept	Total
New	492	222	714
Fresh	18	434	452
Picked	0	0	0
Done	0	11	11
Total	510	667	1177

Error

5.7b

Counts

1177 → 667

Compiler

Compiled 37617 to 17415 computations (53.7% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))
0.1b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
23.0b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64` `sqrt-div_binary64`
22×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `pow1/2_binary64`
9×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow-prod-up_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`diff-log_binary64` `associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `pow-plus_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `pow2_binary64`

Counts

4 → 83

Calls

8 calls:

11.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
7.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))

series595.0ms (0.4%)

Counts

4 → 79

Calls

4 calls:

165.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
147.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
142.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
140.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3171 to 2408 computations (24.1% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5469	3030

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

5.5b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.3b	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0b	(log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.5b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
7.5b	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
13.6b	(-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
23.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
18×	`log-prod_binary64` `exp-sum_binary64`
13×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64`
8×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
7×	`pow1_binary64`
6×	`distribute-lft-out--_binary64` `exp-prod_binary64`
4×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`log-pow_binary64` `distribute-rgt-neg-in_binary64`
2×	`pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `div-exp_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 97

Calls

8 calls:

15.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
14.0ms	(-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

series1.0s (0.7%)

Counts

4 → 67

Calls

4 calls:

413.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
228.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
223.0ms	(-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
142.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3205 to 2142 computations (33.2% saved)

simplify111.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4964	3260
1	4964	3260

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

3.5b	(-.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 a c))) 3) (pow.f64 a 3)) (.f64 3 (/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3))))
3.2b	(.f64 b_2 (neg.f64 (.f64 a c)))
0.3b	(pow.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) 3)
0.1b	(.f64 3 (/.f64 (.f64 b_2 (neg.f64 (*.f64 a c))) (pow.f64 a 3)))
11.4b	(sqrt.f64 (neg.f64 (*.f64 a c)))
15.4b	(/.f64 (pow.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) 3) (pow.f64 a 3))
20.0b	(/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3))
20.2b	(cbrt.f64 (-.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 a c))) 3) (pow.f64 a 3)) (.f64 3 (/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3)))))

rewrite154.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

300×	`times-frac_binary64`
198×	`unpow-prod-down_binary64` `cube-prod_binary64`
162×	`sqrt-prod_binary64`
153×	`add-sqr-sqrt_binary64`
152×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
29×	`add-exp-log_binary64`
27×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
25×	`associate-/l*_binary64`
24×	`associate-/r*_binary64`
15×	`div-exp_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow-to-exp_binary64` `pow-exp_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `prod-exp_binary64` `cbrt-prod_binary64`
2×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-out_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sub-div_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 419

Calls

8 calls:

63.0ms	(cbrt.f64 (-.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 a c))) 3) (pow.f64 a 3)) (.f64 3 (/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3)))))
19.0ms	(/.f64 (pow.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) 3) (pow.f64 a 3))
7.0ms	(/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))
0.0ms	(.f64 3 (/.f64 (.f64 b_2 (neg.f64 (*.f64 a c))) (pow.f64 a 3)))

series580.0ms (0.4%)

Counts

4 → 32

Calls

4 calls:

310.0ms	(cbrt.f64 (-.f64 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 a c))) 3) (pow.f64 a 3)) (.f64 3 (/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3)))))
165.0ms	(/.f64 (.f64 b_2 (neg.f64 (.f64 a c))) (pow.f64 a 3))
66.0ms	(/.f64 (pow.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) 3) (pow.f64 a 3))
38.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))

Compiler

Compiled 1820 to 1547 computations (15% saved)

simplify161.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

451 → 451

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5120	11062

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.1b	(.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))
0.1b	(.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))
0.0b	(+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
2.9b	(/.f64 (*.f64 a c) b_2)
5.4b	(sqrt.f64 (.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.8b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.8b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite63.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-div_binary64`
29×	`flip3--_binary64` `flip--_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
14×	`associate-*l/_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r*_binary64` `sqrt-pow1_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `pow1/3_binary64` `div-exp_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 85

Calls

8 calls:

31.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
5.0ms	(/.f64 (*.f64 a c) b_2)
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)))
0.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))

series995.0ms (0.6%)

Counts

4 → 39

Calls

4 calls:

598.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3)) (.f64 1/3 (.f64 (/.f64 b_2 (/.f64 (.f64 a c) b_2)) (.f64 (pow.f64 (neg.f64 a) 1/3) (pow.f64 c 1/3))))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
138.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
137.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
121.0ms	(/.f64 (*.f64 a c) b_2)

Compiler

Compiled 4728 to 3444 computations (27.2% saved)

simplify131.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4972	5459
1	4972	5459

prune34.5s (22.3%)

Pruning

884 alts after pruning (870 fresh and 14 done)

	Pruned	Kept	Total
New	673	228	901
Fresh	9	642	651
Picked	0	0	0
Done	2	14	16
Total	684	884	1568

Error

5.6b

Counts

1568 → 884

Compiler

Compiled 15090 to 5721 computations (62.1% saved)

simplify1.0s (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5195	67470

regimes28.1s (18.2%)

Compiler: Compiled 173220 to 101000 computations (41.7% saved)

bsearch137.0ms (0.1%)

Steps

Iters

Range

Point

4.188203731107995e+70

5.992238844557805e+70

5.894200455189858e+70

-1.6002196834793597e-280

-1.4113190830337079e-280

-1.4821568082008274e-280

-6.311738356132816e+156

-8.205629525971014e+151

-6.312232056986123e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.2s (0.8%)

Compiler: Compiled 4274 to 3456 computations (19.1% saved)

bsearch59.0ms (0%)

Steps

Iters	Range		Point
8	1.6142651236779968e-62	2.4885385760282085e-59	1.0962098723847624e-60
9	-6.311738356132816e+156	-8.205629525971014e+151	-2.7875763434404928e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.1s (0.7%)

Compiler: Compiled 4158 to 3368 computations (19% saved)

bsearch54.0ms (0%)

Steps

Iters	Range		Point
8	1.6142651236779968e-62	2.4885385760282085e-59	1.6015594875451156e-59
9	-6.311738356132816e+156	-8.205629525971014e+151	-1.2686276298461605e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes667.0ms (0.4%)

Compiler: Compiled 2265 to 1860 computations (17.9% saved)

bsearch51.0ms (0%)

Steps

Iters	Range		Point
8	1.6142651236779968e-62	2.4885385760282085e-59	1.634375766474329e-62
6	-4.601962369814764e-96	-3.8934403381473534e-97	-2.4522605884826868e-96

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes599.0ms (0.4%)

Compiler: Compiled 1941 to 1560 computations (19.6% saved)

bsearch46.0ms (0%)

Steps

Iters	Range		Point
7	1.0500122303718354e-57	1.3823383699408696e-55	1.727440244410573e-56
6	-4.601962369814764e-96	-3.8934403381473534e-97	-4.08032869154156e-96

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes367.0ms (0.2%)

Compiler: Compiled 1896 to 1518 computations (19.9% saved)

bsearch33.0ms (0%)

Steps

Iters	Range		Point
9	4.970098883170481e-256	6.871088252569108e-251	1.442680684528265e-254

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes45.0ms (0%)

Compiler: Compiled 75 to 123 computations (-64% saved)

bsearch26.0ms (0%)

Steps

Iters	Range		Point
8	4.227119612168491e-70	5.1709117828915445e-67	4.2853242449381334e-70

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes26.0ms (0%)

Accuracy

Total 1.3b remaining (19.8%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch10.0ms (0%)

Compiler: Compiled 220 to 155 computations (29.5% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	321
1	144	321

end0.0ms (0%)

sample34.7s (22.4%)

Algorithm

1×

intervals

Results

234.0ms	1128×	body	2048	valid
224.0ms	5182×	body	128	valid
115.0ms	709×	body	1024	valid
109.0ms	407×	body	4096	valid
48.0ms	388×	body	512	valid
35.0ms	798×	body	128	nan
18.0ms	186×	body	256	valid
13.0ms	239×	body	128	invalid

Compiler

Compiled 43947 to 25697 computations (41.5% saved)

Pareto

0.29383975561939774