Details

analyze4.1s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample178.0ms (0.8%)

Algorithm

1×

intervals

Results

34.0ms	182×	body	128	valid
19.0ms	21×	body	2048	valid
18.0ms	24×	body	1024	valid
17.0ms	19×	body	1024	nan
16.0ms	17×	body	2048	nan
14.0ms	72×	body	128	nan
9.0ms	17×	body	512	valid
9.0ms	17×	body	512	nan
4.0ms	12×	body	256	valid
4.0ms	10×	body	256	nan

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-+l+_binary64`
560×	`associate-l_binary64`
528×	`associate-r_binary64`
455×	`distribute-rgt-in_binary64`
449×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	66	61
2	195	61
3	674	61
4	2578	61
5	5617	61

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

52.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	52.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Status

Error

Program

▶

52.2b

(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

Compiler

Compiled 132 to 91 computations (31.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
14.4b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
21.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
35.4b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite642.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

50.4b

Rules

66×	`sqrt-div_binary64`
40×	`associate-*r/_binary64`
39×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`

Counts

4 → 158

Calls

4 calls:

22.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
14.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
13.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
6.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 11279 to 7235 computations (35.9% saved)

series1.5s (6.6%)

Error

26.1b

Counts

4 → 75

Calls

4 calls:

899.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
322.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
100.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
62.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 16758 to 12284 computations (26.7% saved)

simplify243.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

326×	`associate-/l*_binary64`
315×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`
269×	`*-commutative_binary64`
256×	`times-frac_binary64`

Counts

233 → 209

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	728	15348
1	2093	14863
2	5049	14863

prune282.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	194	15	209
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	15	210

Error

26.1b

Counts

210 → 15

Alt Table

Status	Error	Program
	52.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	52.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	59.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	50.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	46.9b	(/.f64 (neg.f64 (+.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F)))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 B (sqrt.f64 2)))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	63.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C)))))
	46.5b	(/.f64 (neg.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
▶	43.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	52.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (+.f64 (.f64 1/2 (/.f64 (.f64 B B) C)) (-.f64 C A)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	52.2b	(/.f64 (neg.f64 1) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (sqrt.f64 (.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)))) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	58.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A (.f64 C (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (.f64 A A) (.f64 C (-.f64 C (.f64 2 A)))))))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (.f64 B B) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	63.4b	(/.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	50.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A)))) (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))

Compiler

Compiled 13328 to 7051 computations (47.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
10.9b	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

rewrite54.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

26.0b

Rules

12×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
6×	`sqrt-prod_binary64`
6×	`sqrt-pow1_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
3.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 557 to 408 computations (26.8% saved)

series37.0ms (0.2%)

Error

26.1b

Counts

2 → 12

Calls

2 calls:

23.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
14.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 478 to 406 computations (15.1% saved)

simplify162.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

580×	`fabs-mul_binary64`
381×	`unsub-neg_binary64`
332×	`associate-/r/_binary64`
300×	`*-commutative_binary64`
260×	`neg-sub0_binary64`

Counts

52 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	698
1	143	676
2	390	676
3	936	676
4	1694	676
5	2384	676
6	2801	676
7	3173	676
8	4453	676
9	4990	676
10	4746	676
11	4808	676
12	4840	676

prune50.0ms (0.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	21	6	27
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	21	21	42

Error

26.0b

Counts

42 → 21

Alt Table

Status	Error	Program
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (.f64 B B) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	43.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A)))) (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))) (sqrt.f64 (sqrt.f64 2)))))
	63.4b	(/.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	42.9b	(neg.f64 (sqrt.f64 (neg.f64 (/.f64 F A))))
	50.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A)))) (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))
	49.0b	(neg.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))) 3)))
	61.8b	(neg.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))) (sqrt.f64 2))))
	52.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	52.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	59.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	50.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	46.9b	(/.f64 (neg.f64 (+.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F)))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 B (sqrt.f64 2)))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	63.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C)))))
	46.5b	(/.f64 (neg.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
✓	43.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	52.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (+.f64 (.f64 1/2 (/.f64 (.f64 B B) C)) (-.f64 C A)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	52.2b	(/.f64 (neg.f64 1) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (sqrt.f64 (.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)))) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	58.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A (.f64 C (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (.f64 A A) (.f64 C (-.f64 C (.f64 2 A)))))))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	43.0b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))))
	49.0b	(neg.f64 (.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) 3))))

Compiler

Compiled 1513 to 1093 computations (27.8% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

10.9b

(sqrt.f64 (neg.f64 (/.f64 F A)))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

23.6b

Rules

30×	`sqrt-prod_binary64`
18×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

3.0ms

(sqrt.f64 (neg.f64 (/.f64 F A)))

Compiler

Compiled 528 to 217 computations (58.9% saved)

series11.0ms (0.1%)

Error

26.0b

Counts

1 → 6

Calls

1 calls:

11.0ms

(sqrt.f64 (neg.f64 (/.f64 F A)))

Compiler

Compiled 176 to 140 computations (20.5% saved)

simplify261.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
673×	`div-sub_binary64`
594×	`unsub-neg_binary64`
544×	`unswap-sqr_binary64`
442×	`neg-sub0_binary64`

Counts

47 → 24

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	115	696
1	201	676
2	373	676
3	576	676
4	1053	676
5	1734	676
6	2095	676
7	2229	676
8	2358	676
9	2511	676
10	2638	671
11	4020	671
12	3583	671
13	4000	671
14	4374	671
15	4437	671
16	4755	671
17	4968	671
18	4705	671

prune46.0ms (0.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	18	6	24
Fresh	3	16	19
Picked	1	0	1
Done	1	0	1
Total	23	22	45

Error

23.6b

Counts

45 → 22

Alt Table

Status	Error	Program
	40.1b	(neg.f64 (*.f64 (fabs.f64 (cbrt.f64 F)) (sqrt.f64 (neg.f64 (/.f64 (cbrt.f64 F) A)))))
	52.2b	(/.f64 (neg.f64 1) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (sqrt.f64 (.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)))) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	43.1b	(neg.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 F A))) (sqrt.f64 (neg.f64 (cbrt.f64 (/.f64 F A))))))
	58.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A (.f64 C (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (.f64 A A) (.f64 C (-.f64 C (.f64 2 A)))))))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	49.0b	(neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (/.f64 F A))) 3)))
	43.0b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (.f64 B B) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	43.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A)))) (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))) (sqrt.f64 (sqrt.f64 2)))))
	61.8b	(neg.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))) (sqrt.f64 2))))
	52.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	52.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	59.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	50.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
▶	39.1b	(neg.f64 (*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 B (sqrt.f64 2)))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	63.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C)))))
	46.5b	(/.f64 (neg.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	52.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (+.f64 (.f64 1/2 (/.f64 (.f64 B B) C)) (-.f64 C A)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	39.3b	(neg.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 A))) (sqrt.f64 (neg.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 A))))))
	63.4b	(/.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	50.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A)))) (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))
	41.4b	(neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 F)) (sqrt.f64 (neg.f64 (/.f64 (sqrt.f64 F) A)))))

Compiler

Compiled 1575 to 1055 computations (33% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(sqrt.f64 (/.f64 -1 A))
0.2b	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

23.6b

Rules

41×	`add-sqr-sqrt_binary64`
36×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

2 → 70

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))
2.0ms	(sqrt.f64 (/.f64 -1 A))

Compiler

Compiled 901 to 610 computations (32.3% saved)

series16.0ms (0.1%)

Error

23.6b

Counts

2 → 9

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))
5.0ms	(sqrt.f64 (/.f64 -1 A))

Compiler

Compiled 285 to 231 computations (18.9% saved)

simplify162.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

804×	`fabs-mul_binary64`
721×	`unsub-neg_binary64`
577×	`div-sub_binary64`
405×	`unswap-sqr_binary64`
386×	`associate-/r*_binary64`

Counts

79 → 36

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1061
1	186	1016
2	438	1013
3	653	1013
4	1294	1013
5	1925	1013
6	2351	1013
7	3167	1013
8	4213	1013
9	4885	1013
10	4912	1013
11	5101	1013

prune54.0ms (0.2%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	4	17	21
Picked	0	1	1
Done	0	0	0
Total	33	25	58

Error

23.6b

Counts

58 → 25

Alt Table

Status	Error	Program
	43.1b	(neg.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 F A))) (sqrt.f64 (neg.f64 (cbrt.f64 (/.f64 F A))))))
	58.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A (.f64 C (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (.f64 A A) (.f64 C (-.f64 C (.f64 2 A)))))))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	49.0b	(neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (neg.f64 (/.f64 F A))) 3)))
	43.0b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))))
	61.8b	(neg.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))) (sqrt.f64 2))))
	52.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	52.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	59.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	39.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (*.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 (cbrt.f64 F)))))
	50.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F))) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	39.1b	(neg.f64 (*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 B (sqrt.f64 2)))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	63.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C)))))
	39.3b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 F)) (.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 (sqrt.f64 F)))))
	46.5b	(/.f64 (neg.f64 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 A F))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	39.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 F)) (cbrt.f64 (sqrt.f64 F))) (*.f64 (sqrt.f64 (/.f64 -1 A)) (cbrt.f64 (sqrt.f64 F)))))
	52.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (+.f64 (.f64 1/2 (/.f64 (.f64 B B) C)) (-.f64 C A)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	52.2b	(/.f64 (neg.f64 1) (/.f64 (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)) (sqrt.f64 (.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4)))) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A))))))
	39.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 F))) (cbrt.f64 (.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 F)))) (cbrt.f64 (*.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 F)))))
	40.8b	(neg.f64 (exp.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 -1 A)) (sqrt.f64 F)))))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (.f64 B B) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
	63.4b	(/.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (.f64 B B) (sqrt.f64 2))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	50.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (pow.f64 (-.f64 A C) 2))) (+.f64 C A)))) (-.f64 (.f64 B B) (.f64 (.f64 C A) 4))))
	46.1b	(neg.f64 (*.f64 (sqrt.f64 F) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 -1 A)) 3))))
	39.4b	(neg.f64 (.f64 (.f64 (sqrt.f64 F) (fabs.f64 (/.f64 (cbrt.f64 -1) (cbrt.f64 A)))) (sqrt.f64 (/.f64 (cbrt.f64 -1) (cbrt.f64 A)))))

Compiler

Compiled 1061 to 745 computations (29.8% saved)

regimes4.7s (21%)

Accuracy

Total 4.2b remaining (14%)

Threshold costs 0b (0%)

Compiler

Compiled 67274 to 46816 computations (30.4% saved)

bsearch21.0ms (0.1%)

Compiler: Compiled 44 to 32 computations (27.3% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

42×	`*-commutative_binary64`
32×	`+-commutative_binary64`
28×	`sub-neg_binary64`
25×	`neg-sub0_binary64`
25×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	412
1	122	412
2	184	412
3	232	412
4	263	412
5	278	412
6	285	412
7	288	412
8	289	412
9	288	412

end19.0ms (0.1%)

Compiler: Compiled 813 to 552 computations (32.1% saved)

sample9.5s (42.8%)

Algorithm

1×

intervals

Results

1.6s	5571×	body	128	valid
1.1s	823×	body	1024	valid
997.0ms	677×	body	2048	valid
984.0ms	817×	body	1024	nan
883.0ms	604×	body	2048	nan
790.0ms	2912×	body	128	nan
549.0ms	566×	body	512	valid
465.0ms	554×	body	512	nan
197.0ms	363×	body	256	valid
194.0ms	332×	body	256	nan

Compiler

Compiled 1039 to 733 computations (29.5% saved)

Iter	Nodes	Cost
0	65	412
1	122	412
2	184	412
3	232	412
4	263	412
5	278	412
6	285	412
7	288	412
8	289	412
9	288	412

Iter	Nodes	Cost
0	65	412
1	122	412
2	184	412
3	232	412
4	263	412
5	278	412
6	285	412
7	288	412
8	289	412
9	288	412

Details

analyze4.1s (18.6%)

sample178.0ms (0.8%)

simplify41.0ms (0.2%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite642.0ms (2.9%)

series1.5s (6.6%)

simplify243.0ms (1.1%)

prune282.0ms (1.3%)

localize7.0ms (0%)

rewrite54.0ms (0.2%)

series37.0ms (0.2%)

simplify162.0ms (0.7%)

prune50.0ms (0.2%)

localize5.0ms (0%)

rewrite38.0ms (0.2%)

series11.0ms (0.1%)

simplify261.0ms (1.2%)

prune46.0ms (0.2%)

localize6.0ms (0%)

rewrite67.0ms (0.3%)

series16.0ms (0.1%)

simplify162.0ms (0.7%)

prune54.0ms (0.2%)

regimes4.7s (21%)

bsearch21.0ms (0.1%)

simplify22.0ms (0.1%)

end19.0ms (0.1%)

sample9.5s (42.8%)

Profiling

Iter	Nodes	Cost
0	65	412
1	122	412
2	184	412
3	232	412
4	263	412
5	278	412
6	285	412
7	288	412
8	289	412
9	288	412