Details

analyze619.0ms (0.6%)

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)

sample46.0ms (0%)

Algorithm

1×

intervals

Results

8.0ms	181×	body	128	valid
5.0ms	26×	body	2048	valid
3.0ms	22×	body	1024	valid
2.0ms	14×	body	512	valid
2.0ms	7×	body	4096	valid
1.0ms	25×	body	128	nan
0.0ms	6×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 30 to 30 computations (0% saved)

simplify163.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	714	21
1	714	21

prune5.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

29.3b

Counts

8 → 5

Compiler

Compiled 15 to 12 computations (20% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.0b	(-.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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (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:

11.0ms	(/.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)

series543.0ms (0.5%)

Counts

4 → 65

Calls

4 calls:

171.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
133.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
122.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
116.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1676 to 1374 computations (18% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	2824
1	4949	2824

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (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:

12.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
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 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

series528.0ms (0.5%)

Counts

4 → 65

Calls

4 calls:

164.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
131.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
121.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1729 to 1427 computations (17.5% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5899	2545

prune1.2s (1.2%)

Pruning

106 alts after pruning (104 fresh and 2 done)

	Pruned	Kept	Total
New	195	101	296
Fresh	0	3	3
Picked	0	0	0
Done	0	2	2
Total	195	106	301

Error

8.3b

Counts

301 → 106

Compiler

Compiled 4758 to 1819 computations (61.8% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(.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 (-.f64 (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))))) b_2) a)
1.5b	(-.f64 (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))))) b_2)
22.4b	(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)))))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

8 calls:

15.0ms	(-.f64 (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))))) b_2)
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)))))
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 (-.f64 (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))))) b_2) a)

series516.0ms (0.5%)

Counts

4 → 68

Calls

4 calls:

140.0ms	(-.f64 (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))))) b_2)
131.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
131.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
114.0ms	(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)))))

Compiler

Compiled 2574 to 1899 computations (26.2% saved)

simplify58.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4928	2363
1	4928	2363

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 c b_2))
0.0b	(*.f64 -1/2 (/.f64 c b_2))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-l_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

1 → 32

Calls

2 calls:

7.0ms	(*.f64 -1/2 (/.f64 c b_2))
0.0ms	(*.f64 -1/2 (/.f64 c b_2))

series60.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

60.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 60 to 72 computations (-20% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5015	369

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.2b	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_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`
5×	`associate-l_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

8 calls:

16.0ms	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
8.0ms	(+.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 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

series540.0ms (0.5%)

Counts

4 → 65

Calls

4 calls:

163.0ms	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
137.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
119.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1883 to 1581 computations (16% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5204	2483

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
1.0b	(-.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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
22.4b	(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))
23.2b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))

rewrite42.0ms (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:

17.0ms	(-.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)

series493.0ms (0.5%)

Counts

4 → 68

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))) b_2)
127.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))
117.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
114.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)))

Compiler

Compiled 1633 to 1356 computations (17% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4902	2403
1	4902	2403

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.4b	(.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.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 (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))))) b_2) a)
22.4b	(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)))))
23.2b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.2b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.2b	(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:

21.0ms	(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 (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))))) b_2) a)

series817.0ms (0.8%)

Counts

4 → 68

Calls

4 calls:

235.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
231.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
220.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
131.0ms	(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 4320 to 2829 computations (34.5% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5018	4396

prune7.5s (7.5%)

Pruning

269 alts after pruning (263 fresh and 6 done)

	Pruned	Kept	Total
New	472	175	647
Fresh	11	88	99
Picked	0	0	0
Done	1	6	7
Total	484	269	753

Error

8.3b

Counts

753 → 269

Compiler

Compiled 14772 to 6160 computations (58.3% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

15.2b	(/.f64 (*.f64 a c) a)
1.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.3b	(/.f64 (/.f64 (.f64 a c) a) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
15.2b	(/.f64 (*.f64 a c) a)
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `diff-log_binary64` `times-frac_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_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 → 71

Calls

8 calls:

9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(/.f64 (*.f64 a c) a)
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 (/.f64 (.f64 a c) a) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))

series419.0ms (0.4%)

Counts

4 → 59

Calls

4 calls:

147.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
126.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.0ms	(/.f64 (*.f64 a c) a)

Compiler

Compiled 1870 to 1371 computations (26.7% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5210	1740

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

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

8.8b	(-.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.3b	(pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2)
0.1b	(/.f64 (-.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2) a)
0.3b	(pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.8b	(-.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2)
23.2b	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`cbrt-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-out--_binary64` `pow-exp_binary64`

Counts

4 → 65

Calls

8 calls:

14.0ms	(-.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2)
6.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2)
4.0ms	(-.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2) a)

series1.2s (1.2%)

Counts

4 → 76

Calls

4 calls:

424.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2)
397.0ms	(-.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3/2) b_2)
216.0ms	(cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
136.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2810 to 2358 computations (16.1% saved)

simplify52.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5043	2729

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2)
1.0b	(-.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 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2) a)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2)
22.4b	(sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1))
23.2b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

8 calls:

19.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2)
10.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1))
6.0ms	(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 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2) a)

series496.0ms (0.5%)

Counts

4 → 68

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1)) b_2)
129.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
120.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3))
112.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3)) 1))

Compiler

Compiled 1741 to 1464 computations (15.9% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4918	2470
1	4918	2470

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 a (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 b_2)))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.0b	(+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 b_2))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 b_2))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`pow1_binary64` `difference-of-squares_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 67

Calls

8 calls:

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

series507.0ms (0.5%)

Counts

4 → 55

Calls

4 calls:

201.0ms	(-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 b_2))
135.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
95.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
76.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2871 to 2003 computations (30.2% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4944	2000
1	4944	2000

prune10.9s (10.9%)

Pruning

454 alts after pruning (443 fresh and 11 done)

	Pruned	Kept	Total
New	361	193	554
Fresh	8	250	258
Picked	0	0	0
Done	0	11	11
Total	369	454	823

Error

8.3b

Counts

823 → 454

Compiler

Compiled 18308 to 8783 computations (52% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.3b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.3b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (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	(-.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 (.f64 b_2 b_2) (.f64 a c)))))

series614.0ms (0.6%)

Counts

4 → 68

Calls

4 calls:

216.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
147.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
124.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1894 to 1532 computations (19.1% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5541	3242

localize2.0ms (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

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

2.3b	(+.f64 (.f64 b_2 b_2) (.f64 a c))
2.2b	(+.f64 (neg.f64 b_2) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))))
0.2b	(.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a))
0.2b	(.f64 (.f64 a c) (*.f64 a c))
2.3b	(+.f64 (.f64 b_2 b_2) (.f64 a c))
7.7b	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
22.4b	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))))
34.3b	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))

rewrite45.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `sqrt-prod_binary64`
8×	`add-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64`
4×	`associate-/r/_binary64`
3×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip--_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` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`

Counts

4 → 106

Calls

8 calls:

12.0ms	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))
10.0ms	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))))
6.0ms	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
4.0ms	(+.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(.f64 (.f64 a c) (*.f64 a c))

series917.0ms (0.9%)

Counts

4 → 71

Calls

4 calls:

354.0ms	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))
266.0ms	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
174.0ms	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))))
123.0ms	(+.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2341 to 1823 computations (22.1% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4944	4142
1	4944	4142

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

2.2b	(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))) b_2)
0.2b	(.f64 (.f64 a c) (*.f64 a c))
0.2b	(pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3)
0.1b	(/.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))) b_2) a)
7.7b	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
22.4b	(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3)))
23.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))
34.3b	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))

rewrite84.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`cbrt-prod_binary64`
100×	`add-sqr-sqrt_binary64`
92×	`times-frac_binary64`
67×	`unpow-prod-down_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
57×	`sqrt-prod_binary64`
51×	`difference-of-squares_binary64`
50×	`cube-prod_binary64`
20×	`sqr-pow_binary64`
10×	`associate-/r/_binary64`
7×	`rem-sqrt-square_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`associate-/r*_binary64`
2×	`cbrt-div_binary64` `associate-/l/_binary64` `flip3--_binary64` `pow1/3_binary64` `cube-div_binary64` `sqrt-pow1_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sqrt-div_binary64`

Counts

4 → 198

Calls

8 calls:

18.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3)))
17.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))
11.0ms	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))
6.0ms	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))) b_2) a)

series1.1s (1.1%)

Counts

4 → 71

Calls

4 calls:

366.0ms	(/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c)))
348.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3))
256.0ms	(-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (*.f64 a c)))
164.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 b_2 4) (.f64 (.f64 a c) (.f64 a c))) (+.f64 (.f64 b_2 b_2) (*.f64 a c))) 3)))

Compiler

Compiled 1868 to 1535 computations (17.8% saved)

simplify130.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5092	8070

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.4b	(.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
0.3b	(/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))))
0.2b	(/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`

Counts

4 → 62

Calls

8 calls:

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)))
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 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

series571.0ms (0.6%)

Counts

4 → 70

Calls

4 calls:

153.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
143.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
137.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 4766 to 2563 computations (46.2% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4932	2098
1	4932	2098

prune24.6s (24.6%)

Pruning

688 alts after pruning (672 fresh and 16 done)

	Pruned	Kept	Total
New	486	255	741
Fresh	21	417	438
Picked	0	0	0
Done	0	16	16
Total	507	688	1195

Error

8.3b

Counts

1195 → 688

Compiler

Compiled 12913 to 3877 computations (70% saved)

simplify594.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5007	43340

regimes22.9s (22.9%)

Compiler: Compiled 63867 to 36318 computations (43.1% saved)

bsearch120.0ms (0.1%)

Steps

Iters

Range

Point

1.8590571521096164e+71

4.564539783386328e+71

3.5125984377002414e+71

-2.0330465372951506e-293

-2.0430013095779102e-303

-2.9200144778223044e-303

-4.0151733111361164e+152

-2.16448946934307e+151

-2.1862957928694407e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes541.0ms (0.5%)

Compiler: Compiled 1536 to 1374 computations (10.5% saved)

bsearch59.0ms (0.1%)

Steps

Iters	Range		Point
10	3.346097554024657e-21	3.423137315093022e-09	8.404990259364683e-21
7	-4.0151733111361164e+152	-2.16448946934307e+151	-4.0217367461644927e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes593.0ms (0.6%)

Compiler: Compiled 1464 to 1320 computations (9.8% saved)

bsearch60.0ms (0.1%)

Steps

Iters	Range		Point
10	3.346097554024657e-21	3.423137315093022e-09	5.5095413459467915e-12
7	-3.9749371964139623e-85	-1.3247591031311836e-86	-1.7726378306444592e-85

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes628.0ms (0.6%)

Compiler: Compiled 1368 to 1236 computations (9.6% saved)

bsearch129.0ms (0.1%)

Steps

Iters	Range		Point
10	3.346097554024657e-21	3.423137315093022e-09	3.3790711201759446e-21
7	2.1496408072214626e-67	4.162023247961021e-65	1.3852823591340843e-66
9	3.875939282865928e-111	5.451056899893752e-103	3.9552053462202354e-103
9	-2.9792079100068955e-53	-4.2220491592285944e-58	-1.6649790089458955e-55

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes663.0ms (0.7%)

Compiler: Compiled 1284 to 1161 computations (9.6% saved)

bsearch64.0ms (0.1%)

Steps

Iters	Range		Point
10	3.346097554024657e-21	3.423137315093022e-09	3.3790711201759446e-21
9	-2.9792079100068955e-53	-4.2220491592285944e-58	-8.785183345378378e-58

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes670.0ms (0.7%)

Compiler: Compiled 1209 to 1086 computations (10.2% saved)

bsearch59.0ms (0.1%)

Steps

Iters	Range		Point
10	3.346097554024657e-21	3.423137315093022e-09	4.029481774360446e-21
7	-3.9749371964139623e-85	-1.3247591031311836e-86	-2.3641434901267597e-86

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes390.0ms (0.4%)

Compiler: Compiled 1164 to 1044 computations (10.3% saved)

bsearch31.0ms (0%)

Steps

Iters	Range		Point
9	8.338938791839915e-226	3.9855442102186e-217	2.5364996268637023e-221

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes48.0ms (0%)

Compiler: Compiled 81 to 135 computations (-66.7% saved)

bsearch31.0ms (0%)

Steps

Iters	Range		Point
9	8.338938791839915e-226	3.9855442102186e-217	1.2785931220637834e-223

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes44.0ms (0%)

Compiler: Compiled 66 to 117 computations (-77.3% saved)

bsearch29.0ms (0%)

Steps

Iters	Range		Point
9	8.338938791839915e-226	3.9855442102186e-217	1.2785931220637834e-223

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes35.0ms (0%)

Compiler: Compiled 36 to 84 computations (-133.3% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
11	-2.0430013095779102e-303	1.5311407354141505e-293	-3.6479611445196e-310

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0%)

Accuracy

Total 1.3b remaining (19.8%)

Threshold costs 0b (0%)

Compiler

Compiled 24 to 69 computations (-187.5% saved)

bsearch13.0ms (0%)

Compiler: Compiled 299 to 218 computations (27.1% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	182	443
1	182	443

end0.0ms (0%)

sample15.8s (15.8%)

Algorithm

1×

intervals

Results

240.0ms	1126×	body	2048	valid
227.0ms	5137×	body	128	valid
120.0ms	763×	body	1024	valid
99.0ms	408×	body	4096	valid
44.0ms	376×	body	512	valid
32.0ms	778×	body	128	nan
15.0ms	190×	body	256	valid
11.0ms	249×	body	128	invalid

Compiler

Compiled 21899 to 12550 computations (42.7% saved)

Pareto

0.2996855130335004