Details

analyze704.0ms (9.4%)

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)

sample1.7s (22.9%)

Results

1.5s	8256×	body	128	valid
179.0ms	1053×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify35.0ms (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

19.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	19.2b	(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))))
▶	19.1b	(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))))))

Status

Error

Program

19.2b

(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))))

▶

19.1b

(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))))))

Compiler

Compiled 231 to 147 computations (36.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series111.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite72.0ms (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

Calls

4 calls:

68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
68.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
68.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
68.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
295×	`fma-def_binary64`
279×	`associate-r_binary64`
278×	`associate-/l*_binary64`
256×	`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

prune554.0ms (7.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	326	8	334
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	327	9	336

Error

6.1b

Counts

336 → 9

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 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 3)))))
▶	19.1b	(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) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	19.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.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 (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))))
	19.1b	(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))))
	29.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.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))))))
	21.8b	(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))))))
	19.2b	(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))))
	21.8b	(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 16619 to 9880 computations (40.5% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	4.7b	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b))))
✓	6.9b	(*.f64 a (/.f64 c b))
	22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series37.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

24.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b))))
13.0ms	(*.f64 a (/.f64 c b))

rewrite54.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`prod-diff_binary64`
138×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
129×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	268	27
2	4001	27

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

52.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b))))
52.0ms	(*.f64 a (/.f64 c b))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

517×	`unswap-sqr_binary64`
513×	`cancel-sign-sub-inv_binary64`
512×	`fma-neg_binary64`
263×	`times-frac_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	1319
1	137	1319
2	504	1271
3	2763	1271

Stop Event

1×	node limit

Counts

141 → 85

prune371.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	195	6	201
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	198	12	210

Error

6.1b

Counts

210 → 12

Alt Table

Status	Error	Program
	36.5b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (.f64 c (.f64 2 (/.f64 1 (+.f64 b (fma.f64 2 (*.f64 a (/.f64 c b)) b))))))
▶	19.1b	(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))))
	19.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.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 (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))))
	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 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 3)))))
	27.1b	(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) (fma.f64 2 (exp.f64 (log.f64 (.f64 a (/.f64 c b)))) (neg.f64 b)))))
	29.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.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))))))
	20.1b	(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) (fma.f64 2 (cbrt.f64 (pow.f64 (.f64 a (/.f64 c b)) 3)) (neg.f64 b)))))
	21.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (*.f64 a (/.f64 c b)) (neg.f64 b)))))
	42.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 b a))
	21.8b	(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) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	19.2b	(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 9855 to 5463 computations (44.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	8.4b	(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
	22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	23.5b	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series75.0ms (1%)

Counts

2 → 56

Calls

2 calls:

40.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)
34.0ms	(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

279×	`fma-def_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
176×	`fma-neg_binary64`
142×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	306	29
2	3734	29

Stop Event

1×	node limit

Counts

2 → 80

Calls

2 calls:

54.0ms	(+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
54.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
252×	`distribute-neg-frac_binary64`
172×	`sub-neg_binary64`
169×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2638
1	752	2580
2	2949	2540

Stop Event

1×	node limit

Counts

136 → 158

prune490.0ms (6.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	271	3	274
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	276	10	286

Error

3.4b

Counts

286 → 10

Alt Table

Status	Error	Program
	19.2b	(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))))
	37.8b	(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 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2))))
	36.3b	(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 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2))))
▶	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 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 3)))))
✓	19.1b	(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))))
	29.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.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))))))
	19.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (*.f64 a (/.f64 c b)) (neg.f64 b)))))
	21.8b	(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) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	36.9b	(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 (fma.f64 (.f64 -1/16 (/.f64 b (/.f64 c b))) (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -4 c)) (log.f64 a))) a) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -4 c)) (log.f64 a)))) 2))))

Compiler

Compiled 15025 to 9522 computations (36.6% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.4b	(+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3)))
	22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	22.9b	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 3))
✓	23.7b	(cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series98.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

35.0ms

(cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))

34.0ms

(+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 3)))

28.0ms

(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 3))

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

342×	`fma-def_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
196×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	294	40
2	3565	40

Stop Event

1×	node limit

Counts

3 → 117

Calls

3 calls:

51.0ms

(+.f64 (neg.f64 b) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 3)))

51.0ms

(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 3))

51.0ms

(cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
465×	`fma-def_binary64`
371×	`associate-/r*_binary64`
362×	`associate-/l*_binary64`
201×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1909
1	457	1887
2	1536	1819

Stop Event

1×	node limit

Counts

169 → 178

prune419.0ms (5.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	226	10	236

Error

3.4b

Counts

236 → 10

Alt Table

Status	Error	Program
	19.2b	(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))))
	37.8b	(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 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2))))
	36.3b	(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 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2))))
✓	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 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 3)))))
✓	19.1b	(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))))
	29.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.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))))))
	19.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.8b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (fma.f64 2 (*.f64 a (/.f64 c b)) (neg.f64 b)))))
	21.8b	(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) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	36.9b	(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 (fma.f64 (.f64 -1/16 (/.f64 b (/.f64 c b))) (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -4 c)) (log.f64 a))) a) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -4 c)) (log.f64 a)))) 2))))

Compiler

Compiled 11037 to 6789 computations (38.5% saved)

regimes2.0s (26.6%)

Accuracy

Total 3.6b remaining (51.7%)

Threshold costs 0b (0%)

Counts

141 → 5

Compiler

Compiled 22818 to 15470 computations (32.2% saved)

bsearch8.0ms (0.1%)

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

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	494
1	74	478
2	104	478
3	126	478
4	140	478
5	146	478
6	147	478

Stop Event

1×

saturated

end332.0ms (4.4%)

Compiler: Compiled 1079 to 664 computations (38.5% saved)

Details

analyze704.0ms (9.4%)

sample1.7s (22.9%)

simplify35.0ms (0.5%)

prune5.0ms (0.1%)

localize19.0ms (0.3%)

series111.0ms (1.5%)

rewrite72.0ms (1%)

simplify47.0ms (0.6%)

prune554.0ms (7.4%)

localize23.0ms (0.3%)

series37.0ms (0.5%)

rewrite54.0ms (0.7%)

simplify40.0ms (0.5%)

prune371.0ms (5%)

localize27.0ms (0.4%)

series75.0ms (1%)

rewrite56.0ms (0.7%)

simplify60.0ms (0.8%)

prune490.0ms (6.6%)

localize29.0ms (0.4%)

series98.0ms (1.3%)

rewrite53.0ms (0.7%)

simplify41.0ms (0.5%)

prune419.0ms (5.6%)

regimes2.0s (26.6%)

bsearch8.0ms (0.1%)

simplify19.0ms (0.3%)

end332.0ms (4.4%)

Profiling