Details

analyze782.0ms (7.9%)

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)

sample2.1s (21.8%)

Results

1.8s	8256×	body	128	valid
218.0ms	1087×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

835×	`rules-20_binary64`
678×	`fma-neg_binary64`
614×	`rules-21_binary64`
371×	`rules-11_binary64`
341×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	126	58
2	360	58
3	1355	54
4	3874	54
5	53	54

prune5.0ms (0%)

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

18.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (/.f64 1/2 a)))

Status

Error

Program

▶

18.8b

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

19.1b

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

Compiler

Compiled 237 to 142 computations (40.1% saved)

localize19.0ms (0.2%)

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))))
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series155.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

59.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
48.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
39.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite133.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
175×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`

Counts

4 → 175

Calls

4 calls:

129.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
129.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
129.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	322	68
2	4204	68
3	4996	65
4	4883	65
0	0	0
1	0	0

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

748×	`rules-40_binary64`
748×	`rules-41_binary64`
748×	`rules-42_binary64`
748×	`rules-43_binary64`
204×	`fma-neg_binary64`

Counts

271 → 230

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	90	2275
1	621	2179
2	2678	2179
3	5014	2179

prune611.0ms (6.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	340	11	351
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	341	12	353

Error

3.1b

Counts

353 → 12

Alt Table

Status	Error	Program
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
▶	18.6b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)))
	19.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (/.f64 1/2 a)))
	21.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))) (*.f64 2 a)))
	25.2b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 -1 b)) (.f64 2 a)))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	24.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	20.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 17843 to 10702 computations (40% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series81.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

81.0ms

(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))

rewrite73.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

279×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
147×	`add-cbrt-cube_binary64`

Counts

1 → 29

Calls

1 calls:

72.0ms

(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	364	26
2	4575	26
3	4898	26
0	0	0
1	0	0

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

570×	`rules-40_binary64`
570×	`rules-41_binary64`
570×	`rules-42_binary64`
570×	`rules-43_binary64`
512×	`rules-15-rev_binary64`

Counts

49 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	634
1	455	608
2	2034	608
3	5308	608

prune441.0ms (4.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	230	5	235
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	234	13	247

Error

3.1b

Counts

247 → 13

Alt Table

Status	Error	Program
▶	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (.f64 2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)))
	18.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	25.1b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (-.f64 (/.f64 c b) (/.f64 b a)))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	25.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 -1 (/.f64 b a)))
	24.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (/.f64 1/2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (pow.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	20.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 10056 to 5865 computations (41.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (*.f64 2 a))
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	21.4b	(pow.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)) 1/4)
✓	23.2b	(fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series305.0ms (3.1%)

Counts

3 → 108

Calls

3 calls:

145.0ms

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

111.0ms

(fma.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))

48.0ms

(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4)

rewrite82.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
152×	`add-cbrt-cube_binary64`

Counts

3 → 90

Calls

3 calls:

79.0ms

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

79.0ms

(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4)

79.0ms

(fma.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 1/4) (neg.f64 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	96
1	384	62
2	4605	62
3	4904	62
0	0	0
1	0	0

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
750×	`rules-41_binary64`
750×	`rules-43_binary64`
748×	`rules-42_binary64`
393×	`rules-40_binary64`

Counts

198 → 251

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	419	6012
1	3132	6012
2	5162	6012

prune1.1s (11.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	457	1	458
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	458	13	471

Error

2.1b

Counts

471 → 13

Alt Table

Status	Error	Program
✓	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (.f64 2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)))
▶	18.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	25.1b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (-.f64 (/.f64 c b) (/.f64 b a)))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b) (.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (/.f64 1/2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (pow.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	24.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	20.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 26444 to 16319 computations (38.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2)))
	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series76.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

76.0ms

(*.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2)))

rewrite83.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

621×	`prod-diff_binary64`
174×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`

Counts

1 → 59

Calls

1 calls:

80.0ms

(*.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	411	26
2	4752	26
3	5829	26
0	0	0
1	0	0

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

570×	`rules-40_binary64`
570×	`rules-41_binary64`
570×	`rules-42_binary64`
570×	`rules-43_binary64`
512×	`rules-15-rev_binary64`

Counts

79 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	634
1	455	608
2	2034	608
3	5308	608

prune914.0ms (9.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	450	0	450
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	450	13	463

Error

2.1b

Counts

463 → 13

Alt Table

Status	Error	Program
✓	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) (neg.f64 b)) (.f64 2 a)))
	29.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a))))) (.f64 2 a)))
✓	18.8b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	23.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 3/2)))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	25.1b	(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (-.f64 (/.f64 c b) (/.f64 b a)))
	18.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b) (.f64 2 a)))
	31.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 c) (sqrt.f64 (-.f64 (/.f64 (.f64 b b) c) (.f64 4 a)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.1b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))))) (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (/.f64 1/2 a)))
	19.0b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) b)) (.f64 (pow.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (*.f64 a 2))))
	24.3b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	20.9b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (neg.f64 (.f64 (.f64 4 a) c))))) 3))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))

Compiler

Compiled 24749 to 14209 computations (42.6% saved)

regimes1.8s (18.7%)

Accuracy

Total 5.6b remaining (76.1%)

Threshold costs 0b (0%)

Counts

127 → 5

Compiler

Compiled 19662 to 13206 computations (32.8% saved)

bsearch59.0ms (0.6%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	493
1	57	493

end548.0ms (5.6%)

Compiler: Compiled 1227 to 757 computations (38.3% saved)

Details

analyze782.0ms (7.9%)

sample2.1s (21.8%)

simplify58.0ms (0.6%)

prune5.0ms (0%)

localize19.0ms (0.2%)

series155.0ms (1.6%)

rewrite133.0ms (1.4%)

simplify70.0ms (0.7%)

prune611.0ms (6.2%)

localize20.0ms (0.2%)

series81.0ms (0.8%)

rewrite73.0ms (0.7%)

simplify40.0ms (0.4%)

prune441.0ms (4.5%)

localize21.0ms (0.2%)

series305.0ms (3.1%)

rewrite82.0ms (0.8%)

simplify110.0ms (1.1%)

prune1.1s (11.1%)

localize22.0ms (0.2%)

series76.0ms (0.8%)

rewrite83.0ms (0.8%)

simplify42.0ms (0.4%)

prune914.0ms (9.3%)

regimes1.8s (18.7%)

bsearch59.0ms (0.6%)

simplify5.0ms (0%)

end548.0ms (5.6%)

Profiling