Details

analyze699.0ms (9.8%)

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)

sample1.6s (22.5%)

Results

1.4s	8256×	body	128	valid
171.0ms	1044×	body	128	invalid

Compiler

Compiled 84 to 54 computations (35.7% saved)

preprocess56.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

623×	`fma-neg_binary64`
569×	`div-sub_binary64`
307×	`fma-def_binary64`
296×	`sub-neg_binary64`
276×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	232
1	143	208
2	409	208
3	940	200
4	1724	200
5	3271	200
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1122×	`fma-def_binary64`
776×	`fma-neg_binary64`
260×	`associate-/l*_binary64`
249×	`cancel-sign-sub-inv_binary64`
205×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	123	52
3	304	50
4	546	50
5	993	50
6	2057	50
7	3568	50
8	4834	50

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

19.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	19.4b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))

Status

Error

Program

▶

19.2b

(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

19.4b

(if (>=.f64 b 0) (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))) (/.f64 -1/2 a)) (*.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) b))))

Compiler

Compiled 231 to 147 computations (36.4% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	2.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series114.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))	a	inf
7.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))	c	inf
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))	b	inf
6.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))	c	-inf
6.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))	a	-inf

rewrite73.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
167×	`egg-rr`
147×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	301	56
2	4302	56

Stop Event

1×	node limit

Counts

4 → 167

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
293×	`fma-def_binary64`
279×	`associate-r_binary64`
278×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2213
1	296	2123
2	973	2035

Stop Event

1×	node limit

Counts

263 → 226

prune577.0ms (8.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	324	10	334
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	325	11	336

Error

5.2b

Counts

336 → 11

Alt Table

Status	Error	Program
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))))))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	37.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (*.f64 a -4))) 1/4) 2))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	19.4b	(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	20.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (*.f64 a (/.f64 c b)) b))))
	20.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (.f64 -1 b))))
	18.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	18.7b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

Compiler

Compiled 16827 to 10009 computations (40.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
	1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	2.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series137.0ms (1.9%)

Counts

1 → 20

Calls

9 calls:

32.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))	a	inf
29.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))	c	inf
27.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))	a	-inf
27.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))	c	-inf
7.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))	b	inf

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	342	22
2	4887	22

Stop Event

1×	node limit

Counts

1 → 45

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-neg_binary64`
473×	`times-frac_binary64`
286×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`
223×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	575
1	213	556
2	701	520
3	4128	520

Stop Event

1×	node limit

Counts

65 → 68

prune421.0ms (5.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	237	5	242
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	242	11	253

Error

5.2b

Counts

253 → 11

Alt Table

Status	Error	Program
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	25.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 3/2)))))
	32.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))))
▶	18.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))))))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	20.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	32.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 2 c)) 2) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (.f64 2 (/.f64 c (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))))))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (*.f64 a -4))) 1/4) 2))))

Compiler

Compiled 9966 to 5836 computations (41.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	4.0b	(/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a))
✓	5.8b	(*.f64 a (/.f64 c b))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series34.0ms (0.5%)

Counts

2 → 72

Calls

18 calls:

3.0ms	(/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a))	a	0
3.0ms	(*.f64 a (/.f64 c b))	a	inf
2.0ms	(/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a))	c	-inf
2.0ms	(/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a))	b	-inf
2.0ms	(/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a))	a	inf

rewrite59.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	292	27
2	4375	27

Stop Event

1×	node limit

Counts

2 → 66

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
461×	`fma-neg_binary64`
327×	`div-sub_binary64`
192×	`associate-/l*_binary64`
173×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	566
1	18	566
2	29	566
3	43	566
4	57	566
5	87	566
6	151	566
7	217	566
8	379	566
9	786	566
10	1728	566
11	2880	566
12	3630	566
13	3846	566
14	4061	566
15	4127	566
16	4167	566
17	4195	566
18	4195	566

Stop Event

1×

saturated

Counts

138 → 71

prune379.0ms (5.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	185	11	196

Error

5.2b

Counts

196 → 11

Alt Table

Status	Error	Program
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	25.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 3/2)))))
	32.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))))
✓	18.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
▶	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))))))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	20.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	32.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 2 c)) 2) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (.f64 2 (/.f64 c (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))))))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (*.f64 a -4))) 1/4) 2))))

Compiler

Compiled 8823 to 4955 computations (43.8% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	22.3b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	22.3b	(sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))
✓	22.9b	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series93.0ms (1.3%)

Counts

3 → 76

Calls

27 calls:

5.0ms	(sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))	c	inf
5.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)	b	0
5.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)	b	inf
4.0ms	(sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))	c	-inf
4.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)	c	inf

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`log-prod_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
182×	`log-pow_binary64`
165×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	108
1	288	38
2	3198	38

Stop Event

1×	node limit

Counts

3 → 87

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
511×	`cancel-sign-sub-inv_binary64`
253×	`distribute-neg-frac_binary64`
168×	`sub-neg_binary64`
167×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3040
1	720	2990
2	2815	2916

Stop Event

1×	node limit

Counts

163 → 132

prune626.0ms (8.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	257	11	268

Error

5.2b

Counts

268 → 11

Alt Table

Status	Error	Program
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	25.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 3/2)))))
	32.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 2 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))))
✓	18.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (fma.f64 (.f64 a (/.f64 c b)) -2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	20.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 -1 (/.f64 c b)))
✓	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))))))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	20.0b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (.f64 2 (-.f64 (.f64 a (/.f64 c b)) b))))
	19.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	32.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 2 c)) 2) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) 2)) (cbrt.f64 (.f64 2 (/.f64 c (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))))))
	19.3b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (*.f64 a -4))) 1/4) 2))))

Compiler

Compiled 19093 to 12038 computations (37% saved)

regimes1.4s (20%)

Accuracy

Total 1.0b remaining (15.1%)

Threshold costs 1.0b (15.1%)

Counts

126 → 5

Compiler

Compiled 19474 to 12946 computations (33.5% saved)

bsearch7.0ms (0.1%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.0ms	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.0ms	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.0ms	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Steps

Iters	Point		Range
9.247928143635154e+250	∈ [	9.247928143635154e+250	,	2.4137059065588967e+253	]
0.0	∈ [	0.0	,	4.4069921777477e-303	]
-1.8036196670801813e-254	∈ [	-1.8036196670801813e-254	,	-1.463803794998371e-261	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-3.174033390139873e+307	]

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
19×	`+-commutative_binary64`
15×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	497
1	89	481
2	119	481
3	141	481
4	156	481
5	164	481
6	166	481

Stop Event

1×

saturated

end358.0ms (5%)

Stop Event

1×

fuel

Compiler

Compiled 1096 to 689 computations (37.1% saved)

Details

analyze699.0ms (9.8%)

sample1.6s (22.5%)

preprocess56.0ms (0.8%)

simplify39.0ms (0.5%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

series114.0ms (1.6%)

rewrite73.0ms (1%)

simplify47.0ms (0.6%)

prune577.0ms (8.1%)

localize20.0ms (0.3%)

series137.0ms (1.9%)

rewrite56.0ms (0.8%)

simplify38.0ms (0.5%)

prune421.0ms (5.9%)

localize24.0ms (0.3%)

series34.0ms (0.5%)

rewrite59.0ms (0.8%)

simplify81.0ms (1.1%)

prune379.0ms (5.3%)

localize30.0ms (0.4%)

series93.0ms (1.3%)

rewrite49.0ms (0.7%)

simplify67.0ms (0.9%)

prune626.0ms (8.7%)

regimes1.4s (20%)

bsearch7.0ms (0.1%)

simplify14.0ms (0.2%)

end358.0ms (5%)

Profiling