Details

analyze758.0ms (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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.8s (19.5%)

Results

1.5s	8256×	body	128	valid
201.0ms	1090×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify153.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1753×	`fma-neg_binary64`
1288×	`fma-def_binary64`
631×	`div-sub_binary64`
512×	`times-frac_binary64`
430×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	118	52
3	269	50
4	429	50
5	743	50
6	1315	50
7	1738	50
8	2176	50
9	2853	50
10	4066	50
11	3523	50
12	3575	50
13	3543	50
14	3557	50
15	4510	50
16	4622	50
17	4761	50

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

20.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 149 to 91 computations (38.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series414.0ms (4.4%)

Counts

4 → 80

Calls

4 calls:

264.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
56.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
50.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
43.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify137.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-neg-in_binary64`
159×	`distribute-rgt-in_binary64`
157×	`distribute-lft-neg-in_binary64`

Counts

186 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	5384
1	686	4516
2	2546	4321
3	4500	4319
4	4865	4319

prune447.0ms (4.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	262	16	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	263	16	279

Error

6.0b

Counts

279 → 16

Alt Table

Status	Error	Program
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	34.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 c 2) (.f64 c 2)) (.f64 c 2)) (.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	34.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (log.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
▶	20.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	23.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	28.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	31.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	24.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	23.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	22.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))

Compiler

Compiled 14107 to 8299 computations (41.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 -1/2 (/.f64 (+.f64 b b) a))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-r_binary64`
37×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

1 → 61

Calls

1 calls:

12.0ms

(*.f64 -1/2 (/.f64 (+.f64 b b) a))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
572×	`associate-/r/_binary64`
399×	`*-commutative_binary64`
243×	`distribute-rgt-in_binary64`
242×	`associate-/l*_binary64`

Counts

85 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	111	889
1	254	771
2	684	771
3	2039	771
4	4082	771
5	4938	771

prune549.0ms (5.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	259	8	267
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	265	18	283

Error

6.0b

Counts

283 → 18

Alt Table

Status	Error	Program
	23.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))
	23.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	28.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.1b	(if (>=.f64 b 0) (.f64 (.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)) (.f64 (cbrt.f64 -1/2) (/.f64 (+.f64 b b) a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	24.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b)))
	34.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (log.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	29.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	28.1b	(if (>=.f64 b 0) (exp.f64 (log.f64 (neg.f64 (/.f64 b a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	23.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (/.f64 2 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	22.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 (.f64 -1/2 (cbrt.f64 b)) (/.f64 (+.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	24.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))) (cbrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	33.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (.f64 (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (sqrt.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
▶	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))

Compiler

Compiled 11206 to 6101 computations (45.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	0.8b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series266.0ms (2.8%)

Counts

1 → 20

Calls

1 calls:

266.0ms

(*.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
18×	`add-cube-cbrt_binary64`

Counts

1 → 67

Calls

1 calls:

14.0ms

(*.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
480×	`associate-*l/_binary64`
418×	`associate-/l/_binary64`
406×	`associate-/r*_binary64`
360×	`associate-*r/_binary64`

Counts

87 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2525
1	449	2281
2	1644	2171
3	4562	2171
4	5058	2171

prune940.0ms (10%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	329	3	332
Fresh	4	13	17
Picked	0	1	1
Done	0	0	0
Total	333	17	350

Error

6.0b

Counts

350 → 17

Alt Table

Status	Error	Program
	23.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))
	23.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	28.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.1b	(if (>=.f64 b 0) (.f64 (.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)) (.f64 (cbrt.f64 -1/2) (/.f64 (+.f64 b b) a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
▶	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b))))
	34.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (log.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	29.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	28.1b	(if (>=.f64 b 0) (exp.f64 (log.f64 (neg.f64 (/.f64 b a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	24.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) 1) (.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) (cbrt.f64 c))))
	22.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 (.f64 -1/2 (cbrt.f64 b)) (/.f64 (+.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	35.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))) (.f64 (sqrt.f64 c) (sqrt.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))))
✓	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))

Compiler

Compiled 17102 to 10345 computations (39.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	7.6b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	24.5b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series138.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

82.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
56.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`

Counts

2 → 29

Calls

2 calls:

2.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
2.0ms	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify134.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
395×	`associate-r_binary64`
351×	`times-frac_binary64`
277×	`associate-l_binary64`
267×	`associate-/r*_binary64`

Counts

101 → 151

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	373	6108
1	1265	5483
2	4751	5483
3	5331	5483

prune1.1s (11.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	337	18	355

Error

6.0b

Counts

355 → 18

Alt Table

Status	Error	Program
	35.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (.f64 a -4)) (log.f64 c)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	23.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (*.f64 b -2)))
	23.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	28.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.1b	(if (>=.f64 b 0) (.f64 (.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)) (.f64 (cbrt.f64 -1/2) (/.f64 (+.f64 b b) a))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
✓	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b))))
	34.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (exp.f64 (log.f64 (/.f64 (.f64 2 c) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	20.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	29.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 3)) b)))
	28.1b	(if (>=.f64 b 0) (exp.f64 (log.f64 (neg.f64 (/.f64 b a)))) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	25.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))))
	21.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	24.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) 1) (.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) (cbrt.f64 c))))
	22.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.0b	(if (>=.f64 b 0) (.f64 (.f64 -1/2 (cbrt.f64 b)) (/.f64 (+.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	35.1b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))) (.f64 (sqrt.f64 c) (sqrt.f64 (/.f64 2 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))))))
✓	20.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c 1) (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))

Compiler

Compiled 23858 to 14755 computations (38.2% saved)

regimes1.8s (18.6%)

Accuracy

Total 1.1b remaining (15.4%)

Threshold costs 0b (0%)

Counts

141 → 5

Compiler

Compiled 23258 to 15234 computations (34.5% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	446
1	58	434
2	81	434
3	98	434
4	109	434
5	114	434
6	115	434
7	114	434

end455.0ms (4.8%)

Compiler: Compiled 1337 to 845 computations (36.8% saved)

Details

analyze758.0ms (8%)

sample1.8s (19.5%)

simplify153.0ms (1.6%)

prune4.0ms (0%)

localize19.0ms (0.2%)

series414.0ms (4.4%)

rewrite23.0ms (0.2%)

simplify137.0ms (1.5%)

prune447.0ms (4.7%)

localize19.0ms (0.2%)

series6.0ms (0.1%)

rewrite17.0ms (0.2%)

simplify68.0ms (0.7%)

prune549.0ms (5.8%)

localize22.0ms (0.2%)

series266.0ms (2.8%)

rewrite22.0ms (0.2%)

simplify89.0ms (0.9%)

prune940.0ms (10%)

localize24.0ms (0.3%)

series138.0ms (1.5%)

rewrite5.0ms (0.1%)

simplify134.0ms (1.4%)

prune1.1s (11.6%)

regimes1.8s (18.6%)

bsearch8.0ms (0.1%)

simplify17.0ms (0.2%)

end455.0ms (4.8%)

Profiling