Details

analyze839.0ms (11.3%)

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)

sample1.9s (26.1%)

Results

1.7s	8256×	body	128	valid
218.0ms	1110×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary64`
464×	`times-frac_binary64`
353×	`div-sub_binary64`
283×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	44	52
2	99	52
3	240	50
4	439	50
5	780	50
6	1493	50
7	2856	50
8	4302	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

18.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.3b	(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)))
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))

Status

Error

Program

▶

18.3b

(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)))

18.4b

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

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
✓	0.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series232.0ms (3.1%)

Counts

4 → 80

Calls

4 calls:

124.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
46.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
31.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
31.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
173×	`add-cbrt-cube_binary64`
169×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	81
1	367	67

Stop Event

1×	node limit

Counts

4 → 154

Calls

4 calls:

43.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
43.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
43.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

877×	`times-frac_binary64`
532×	`associate-/l*_binary64`
438×	`fma-def_binary64`
172×	`cancel-sign-sub-inv_binary64`
156×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2470
1	425	2414
2	1471	2285

Stop Event

1×	node limit

Counts

234 → 230

prune426.0ms (5.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	268	9	277
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	269	10	279

Error

6.2b

Counts

279 → 10

Alt Table

Status	Error	Program
	31.9b	(if (>=.f64 b 0) (.f64 2 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) c))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c 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 c (.f64 2 (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	19.6b	(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)))
	36.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (-.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)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.5b	(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 (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)))
	22.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (fma.f64 (.f64 (/.f64 c b) a) -2 b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
▶	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))
	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3))) (/.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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (*.f64 2 a)))

Compiler

Compiled 13767 to 8294 computations (39.8% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))))
✓	0.5b	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
✓	1.0b	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
✓	20.5b	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series220.0ms (3%)

Counts

4 → 80

Calls

4 calls:

122.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))))
41.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
32.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
25.0ms	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

rewrite75.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
150×	`egg-rr`
148×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	312	67
2	4245	67

Stop Event

1×	node limit

Counts

4 → 150

Calls

4 calls:

71.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))))
71.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
71.0ms	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
71.0ms	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
529×	`associate-/l*_binary64`
438×	`associate-/r*_binary64`
384×	`fma-def_binary64`
188×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	395	2390
2	1346	2267

Stop Event

1×	node limit

Counts

230 → 226

prune437.0ms (5.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	270	2	272
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	272	10	282

Error

6.2b

Counts

282 → 10

Alt Table

Status	Error	Program
	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)) 1/4) 2)) (/.f64 -1/2 a)))
	31.9b	(if (>=.f64 b 0) (.f64 2 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) c))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	36.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (-.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)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.5b	(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 (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)))
	19.6b	(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)))
	22.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (fma.f64 (.f64 (/.f64 c b) a) -2 b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3))) (/.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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (*.f64 2 a)))
▶	18.2b	(if (>=.f64 b 0) (.f64 c (/.f64 1 (.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) -1/2))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))

Compiler

Compiled 12777 to 7548 computations (40.9% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
	1.0b	(-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b))))
	20.5b	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))
✓	20.5b	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series63.0ms (0.8%)

Counts

2 → 40

Calls

2 calls:

37.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
26.0ms	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

945×	`prod-diff_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
104×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	210	29
2	2688	29

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

43.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
43.0ms	(sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

441×	`times-frac_binary64`
423×	`fma-neg_binary64`
274×	`associate-/l*_binary64`
266×	`associate-r_binary64`
242×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1112
1	242	1094
2	777	1036
3	4318	1036

Stop Event

1×	node limit

Counts

98 → 103

prune339.0ms (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	215	10	225

Error

6.2b

Counts

225 → 10

Alt Table

Status	Error	Program
▶	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)) 1/4) 2)) (/.f64 -1/2 a)))
	31.9b	(if (>=.f64 b 0) (.f64 2 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) c))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	36.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (-.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)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.5b	(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 (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)))
	19.6b	(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)))
	22.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (fma.f64 (.f64 (/.f64 c b) a) -2 b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3))) (/.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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (*.f64 2 a)))
✓	18.2b	(if (>=.f64 b 0) (.f64 c (/.f64 1 (.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) -1/2))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))

Compiler

Compiled 10729 to 6544 computations (39% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2)
✓	11.0b	(-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2))
	20.5b	(sqrt.f64 (fma.f64 c (/.f64 a -1/4) (*.f64 b b)))
✓	21.1b	(pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series126.0ms (1.7%)

Counts

3 → 92

Calls

3 calls:

52.0ms	(pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2)
39.0ms	(pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4)
35.0ms	(-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2))

rewrite75.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
225×	`log1p-udef_binary64`
138×	`egg-rr`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	282	43
2	3305	43

Stop Event

1×	node limit

Counts

3 → 138

Calls

3 calls:

70.0ms	(pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2)
70.0ms	(-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2))
70.0ms	(pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4)

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

301×	`times-frac_binary64`
272×	`associate-/r*_binary64`
271×	`sub-neg_binary64`
232×	`associate-/l*_binary64`
228×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	312	4491
1	1086	4395
2	4462	4395

Stop Event

1×	node limit

Counts

230 → 272

prune685.0ms (9.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	316	2	318
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	316	12	328

Error

3.4b

Counts

328 → 12

Alt Table

Status	Error	Program
✓	18.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (*.f64 b b)) 1/4) 2)) (/.f64 -1/2 a)))
	31.9b	(if (>=.f64 b 0) (.f64 2 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) c))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	22.8b	(if (>=.f64 b 0) (.f64 -1 (/.f64 c b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	36.0b	(if (>=.f64 b 0) (.f64 (/.f64 (.f64 c 2) (-.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)))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a)))
	18.5b	(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 (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)))
	19.6b	(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)))
	22.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (fma.f64 (.f64 (/.f64 c b) a) -2 b))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
	31.5b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (/.f64 -1/2 a)))
	29.4b	(if (>=.f64 b 0) (/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b))))) (.f64 (-.f64 b (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (/.f64 -1/2 a)))
	18.7b	(if (>=.f64 b 0) (/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3))) (/.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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) 3)) (*.f64 2 a)))
✓	18.2b	(if (>=.f64 b 0) (.f64 c (/.f64 1 (.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) -1/2))) (.f64 (-.f64 b (sqrt.f64 (fma.f64 c (/.f64 a -1/4) (.f64 b b)))) (/.f64 -1/2 a)))

Compiler

Compiled 20329 to 12679 computations (37.6% saved)

regimes1.1s (15.3%)

Accuracy

Total 3.3b remaining (50.4%)

Threshold costs 0b (0%)

Counts

103 → 3

Compiler

Compiled 16098 to 10726 computations (33.4% saved)

bsearch74.0ms (1%)

Steps

Iters	Range		Point
8	8.446472792482571e+138	8.918395576025334e+141	4.146119655255326e+140
9	-5.5848513673766546e+73	-4.4186554162570763e+64	-5.5012097508234716e+73

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
17×	`+-commutative_binary64`
14×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	155
1	77	153
2	106	153
3	129	153
4	143	153
5	149	153
6	150	153

Stop Event

1×

saturated

end312.0ms (4.2%)

Compiler: Compiled 707 to 460 computations (34.9% saved)

Details

analyze839.0ms (11.3%)

sample1.9s (26.1%)

simplify34.0ms (0.5%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

series232.0ms (3.1%)

rewrite47.0ms (0.6%)

simplify49.0ms (0.7%)

prune426.0ms (5.7%)

localize19.0ms (0.3%)

series220.0ms (3%)

rewrite75.0ms (1%)

simplify47.0ms (0.6%)

prune437.0ms (5.9%)

localize31.0ms (0.4%)

series63.0ms (0.8%)

rewrite45.0ms (0.6%)

simplify46.0ms (0.6%)

prune339.0ms (4.6%)

localize25.0ms (0.3%)

series126.0ms (1.7%)

rewrite75.0ms (1%)

simplify86.0ms (1.2%)

prune685.0ms (9.2%)

regimes1.1s (15.3%)

bsearch74.0ms (1%)

simplify7.0ms (0.1%)

end312.0ms (4.2%)

Profiling