Details

analyze1.0s (12.8%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample43.0ms (0.5%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
2.0ms	22×	body	128	nan
1.0ms	14×	body	128	invalid

Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify542.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

1534×	`div-sub_binary64`
1283×	`associate-/l*_binary64`
1224×	`distribute-rgt-in_binary64`
767×	`associate-/r*_binary64`
744×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	43	56
2	91	56
3	198	54
4	309	54
5	519	54
6	918	54
7	1356	54
8	1505	54
9	2181	54
10	2806	54
11	2812	54
12	2814	54
13	2776	54
14	2800	54
15	3982	54
16	3118	54
17	3126	54
18	3134	54
19	3134	54
20	3142	54
21	3142	54
22	3944	54
23	2934	54
24	3120	54
25	3086	54
26	3090	54
27	3102	54
28	3106	54
29	3106	54
30	3268	54
31	3196	54
32	3324	54
33	3428	54
34	3532	54
35	3636	54
36	3036	54
37	3036	54
38	3056	54
39	3092	54
40	3094	54
41	3094	54
42	2785	54

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

20.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	20.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 117 to 75 computations (35.9% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite133.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

20.3b

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 59

Calls

4 calls:

6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 2605 to 1530 computations (41.3% saved)

series172.0ms (2.1%)

Error

6.5b

Counts

4 → 60

Calls

4 calls:

42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
38.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
37.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 4725 to 3210 computations (32.1% saved)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-l_binary64`
634×	`associate-r_binary64`
634×	`times-frac_binary64`
273×	`associate-/r*_binary64`
253×	`associate-/l*_binary64`

Counts

119 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2085
1	333	2006
2	971	2003
3	5364	2003

prune190.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Error

12.2b

Counts

91 → 12

Alt Table

Status	Error	Program
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	28.0b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 b b))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (*.f64 2 a)))
	30.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))) 3)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	29.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 2 a)))
	32.8b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 c a) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))))))) b) (*.f64 2 a)))
	20.4b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	20.6b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3)) b) (.f64 2 a)))
	20.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
▶	20.4b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 3573 to 2132 computations (40.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.1b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite167.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

4 → 56

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
2.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))

Compiler

Compiled 3352 to 1847 computations (44.9% saved)

series188.0ms (2.3%)

Error

6.4b

Counts

4 → 53

Calls

4 calls:

43.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))))
33.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
32.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
31.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5586 to 3635 computations (34.9% saved)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

568×	`times-frac_binary64`
477×	`cancel-sign-sub-inv_binary64`
247×	`*-commutative_binary64`
241×	`associate-/l*_binary64`
239×	`distribute-neg-frac_binary64`

Counts

109 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1815
1	360	1778
2	982	1763
3	3539	1763
4	5075	1763

prune112.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	64	10	74

Error

6.4b

Counts

74 → 10

Alt Table

Status	Error	Program
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	22.1b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (.f64 b 2))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (*.f64 2 a)))
	29.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 2 a)))
	32.8b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 c a) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))))))) b) (*.f64 2 a)))
▶	20.4b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	20.6b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3)) b) (.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 c a)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 3347 to 1976 computations (41% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.1b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite153.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

6.4b

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

4 → 60

Calls

4 calls:

13.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 3569 to 1967 computations (44.9% saved)

series180.0ms (2.2%)

Error

6.4b

Counts

4 → 54

Calls

4 calls:

37.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a)))))) b)
36.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
31.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))
30.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 c a))))

Compiler

Compiled 5891 to 3839 computations (34.8% saved)

simplify111.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

677×	`times-frac_binary64`
281×	`div-sub_binary64`
264×	`associate-/l*_binary64`
260×	`associate-/r*_binary64`
245×	`*-commutative_binary64`

Counts

114 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2135
1	382	2047
2	1056	2044
3	3984	2032
4	4861	2032
5	5350	2032

prune123.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Error

6.4b

Counts

87 → 8

Alt Table

Status	Error	Program
▶	20.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	22.1b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (.f64 b 2))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	29.0b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (*.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)))
	32.8b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 c a) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))))))) b) (*.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 c a)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 3972 to 2359 computations (40.6% saved)

localize38.0ms (0.5%)

Local error

Found 4 expressions with local error:

24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite279.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

6.4b

Rules

12×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`sqrt-div_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 4775 to 2794 computations (41.5% saved)

series208.0ms (2.6%)

Error

6.4b

Counts

4 → 51

Calls

4 calls:

45.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
35.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
35.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
35.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 8770 to 5562 computations (36.6% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`times-frac_binary64`
490×	`associate-l_binary64`
472×	`associate-r_binary64`
333×	`unswap-sqr_binary64`
239×	`distribute-neg-frac_binary64`

Counts

111 → 71

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	2012
1	221	1952
2	680	1952
3	3859	1952
4	4952	1952

prune138.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Error

6.4b

Counts

79 → 8

Alt Table

Status	Error	Program
	25.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))) 3))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	22.1b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (.f64 b 2))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	29.0b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (/.f64 (.f64 c (.f64 a -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (*.f64 2 a)))
	20.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))) b) (.f64 2 a)))
	32.8b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 c a)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 c a) (+.f64 (.f64 4 (.f64 c a)) (.f64 b b))))))) b) (*.f64 2 a)))
	22.3b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 c a)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 5333 to 3152 computations (40.9% saved)

regimes2.2s (27%)

Accuracy

Total 1.2b remaining (16.8%)

Threshold costs 0b (0%)

Compiler

Compiled 30450 to 19234 computations (36.8% saved)

bsearch86.0ms (1.1%)

Steps

Iters	Range		Point
9	9.29811862087418e+117	1.3247104836150403e+126	9.155679788397841e+120
10	-1.7383145377063383e+64	-4.384422854155201e+53	-1.7157042027839432e+64

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
11×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	148
1	56	148
2	68	148
3	85	148
4	94	148
5	100	148
6	102	148
7	101	148

end2.0ms (0%)

Compiler: Compiled 102 to 65 computations (36.3% saved)

sample1.7s (20.6%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
67.0ms	657×	body	128	nan
43.0ms	360×	body	128	invalid

Compiler

Compiled 527 to 340 computations (35.5% saved)

Details

analyze1.0s (12.8%)

sample43.0ms (0.5%)

simplify542.0ms (6.7%)

prune3.0ms (0%)

localize21.0ms (0.3%)

rewrite133.0ms (1.6%)

series172.0ms (2.1%)

simplify68.0ms (0.8%)

prune190.0ms (2.4%)

localize27.0ms (0.3%)

rewrite167.0ms (2.1%)

series188.0ms (2.3%)

simplify81.0ms (1%)

prune112.0ms (1.4%)

localize27.0ms (0.3%)

rewrite153.0ms (1.9%)

series180.0ms (2.2%)

simplify111.0ms (1.4%)

prune123.0ms (1.5%)

localize38.0ms (0.5%)

rewrite279.0ms (3.5%)

series208.0ms (2.6%)

simplify92.0ms (1.1%)

prune138.0ms (1.7%)

regimes2.2s (27%)

bsearch86.0ms (1.1%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample1.7s (20.6%)

Profiling