Details

analyze641.0ms (9%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	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)

simplify602.0ms (8.5%)

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

prune13.0ms (0.2%)

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)

localize24.0ms (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)

rewrite171.0ms (2.4%)

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:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 2605 to 1530 computations (41.3% saved)

series226.0ms (3.2%)

Error

6.5b

Counts

4 → 60

Calls

4 calls:

56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
49.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
47.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
38.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 4725 to 3210 computations (32.1% saved)

simplify143.0ms (2%)

Algorithm

1×	egg-herbie

Rules

634×	`times-frac_binary64`
273×	`associate-/r*_binary64`
253×	`associate-/l*_binary64`
236×	`unswap-sqr_binary64`
232×	`*-commutative_binary64`

Counts

119 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2073
1	331	1994
2	1029	1991
3	3935	1991
4	4911	1991
5	4972	1991
6	4909	1991

prune151.0ms (2.1%)

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
	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 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.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 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 a (.f64 c -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 a c))) 3)))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 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 a c)))) 3))))) (/.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)))
	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 a c)))) 3)) 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 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))))))) 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)))
	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 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 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 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 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 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a)))

Compiler

Compiled 3549 to 2128 computations (40% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite219.0ms (3.1%)

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:

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

Compiler

Compiled 3352 to 1847 computations (44.9% saved)

series246.0ms (3.5%)

Error

6.4b

Counts

4 → 53

Calls

4 calls:

50.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
40.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5586 to 3635 computations (34.9% saved)

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

583×	`times-frac_binary64`
468×	`cancel-sign-sub-inv_binary64`
243×	`*-commutative_binary64`
241×	`associate-/l*_binary64`
239×	`distribute-neg-frac_binary64`

Counts

109 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1815
1	320	1778
2	986	1763
3	3561	1763
4	5074	1763

prune158.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Error

6.4b

Counts

72 → 10

Alt Table

Status	Error	Program
	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 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.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)))
	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 a c)))) 3))))) (/.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)))
	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 a c)))) 3)) 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 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 4 (.f64 a c)) (.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 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 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 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))

Compiler

Compiled 3331 to 1973 computations (40.8% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite184.0ms (2.6%)

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:

15.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3569 to 1967 computations (44.9% saved)

series247.0ms (3.5%)

Error

6.4b

Counts

4 → 54

Calls

4 calls:

50.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
49.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
41.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
40.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5891 to 3839 computations (34.8% saved)

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

114 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2090
1	344	2047
2	1059	2044
3	4007	2032
4	4850	2032
5	5351	2032

prune150.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	67	10	77

Error

6.4b

Counts

77 → 10

Alt Table

Status	Error	Program
	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 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.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)))
	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 a c)))) 3))))) (/.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)))
	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 a c)))) 3)) 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 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 4 (.f64 a c)) (.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 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 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 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))

Compiler

Compiled 3606 to 2145 computations (40.5% saved)

localize37.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 1530 to 1275 computations (16.7% saved)

rewrite202.0ms (2.8%)

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:

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

Compiler

Compiled 4047 to 2198 computations (45.7% saved)

series264.0ms (3.7%)

Error

6.4b

Counts

4 → 51

Calls

4 calls:

56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
45.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 7353 to 4550 computations (38.1% saved)

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

583×	`times-frac_binary64`
567×	`distribute-rgt-neg-in_binary64`
346×	`cancel-sign-sub-inv_binary64`
241×	`associate-/l*_binary64`
239×	`distribute-neg-frac_binary64`

Counts

111 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	107	2000
1	242	1952
2	794	1952
3	3076	1952
4	4957	1952
5	5039	1952

prune149.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	56	10	66

Error

6.4b

Counts

66 → 10

Alt Table

Status	Error	Program
	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 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.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)))
	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 a c)))) 3))))) (/.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)))
	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 a c)))) 3)) 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 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 4 (.f64 a c)) (.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 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))
	35.2b	(if (>=.f64 b 0) (.f64 -2 (/.f64 c (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 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 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 2 a)))

Compiler

Compiled 3776 to 2180 computations (42.3% saved)

regimes1.3s (18.6%)

Accuracy

Total 1.2b remaining (16.9%)

Threshold costs 0b (0%)

Compiler

Compiled 18802 to 11918 computations (36.6% saved)

bsearch69.0ms (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)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
14×	`sub-neg_binary64`
13×	`+-commutative_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	150
1	62	150
2	83	150
3	101	150
4	113	150
5	118	150
6	119	150
7	118	150

end3.0ms (0%)

Compiler: Compiled 103 to 64 computations (37.9% saved)

sample1.5s (20.5%)

Algorithm

1×

intervals

Results

694.0ms	8000×	body	128	valid
52.0ms	657×	body	128	nan
29.0ms	360×	body	128	invalid

Compiler

Compiled 596 to 383 computations (35.7% saved)

Details

analyze641.0ms (9%)

sample39.0ms (0.6%)

simplify602.0ms (8.5%)

prune13.0ms (0.2%)

localize24.0ms (0.3%)

rewrite171.0ms (2.4%)

series226.0ms (3.2%)

simplify143.0ms (2%)

prune151.0ms (2.1%)

localize32.0ms (0.5%)

rewrite219.0ms (3.1%)

series246.0ms (3.5%)

simplify86.0ms (1.2%)

prune158.0ms (2.2%)

localize32.0ms (0.4%)

rewrite184.0ms (2.6%)

series247.0ms (3.5%)

simplify120.0ms (1.7%)

prune150.0ms (2.1%)

localize37.0ms (0.5%)

rewrite202.0ms (2.8%)

series264.0ms (3.7%)

simplify105.0ms (1.5%)

prune149.0ms (2.1%)

regimes1.3s (18.6%)

bsearch69.0ms (1%)

simplify9.0ms (0.1%)

end3.0ms (0%)

sample1.5s (20.5%)

Profiling