Details

analyze758.0ms (8.4%)

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)

sample1.8s (20.2%)

Results

1.6s	8256×	body	128	valid
201.0ms	1108×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify37.0ms (0.4%)

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

17.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.0b	(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))))))
	18.1b	(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

▶

18.0b

(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))))))

18.1b

(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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series103.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
32.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
26.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite69.0ms (0.8%)

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:

65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
65.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
65.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify51.0ms (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

prune668.0ms (7.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	322	12	334
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	323	13	336

Error

4.6b

Counts

336 → 13

Alt Table

Status	Error	Program
	18.1b	(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 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 2))))))
	18.2b	(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) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	29.1b	(if (>=.f64 b 0) (/.f64 (/.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)))))) (.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) (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))))))
	18.1b	(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) (.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)))))))))
	20.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.6b	(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 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	21.9b	(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) (.f64 -1 b))))
	19.5b	(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))))))
	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) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))))))
	28.6b	(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 (neg.f64 b) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))))
▶	18.0b	(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))))))
	18.1b	(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 16981 to 10118 computations (40.4% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	9.4b	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
	20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	21.3b	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series75.0ms (0.8%)

Counts

2 → 56

Calls

2 calls:

40.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)
35.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))

rewrite111.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`prod-diff_binary64`
196×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	307	29
2	3736	29

Stop Event

1×	node limit

Counts

2 → 196

Calls

2 calls:

102.0ms	(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4) 2))
102.0ms	(pow.f64 (fma.f64 b b (.f64 c (.f64 a -4))) 1/4)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-def_binary64`
482×	`cancel-sign-sub-inv_binary64`
244×	`distribute-neg-frac_binary64`
177×	`sub-neg_binary64`
169×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2538
1	759	2480
2	2968	2444

Stop Event

1×	node limit

Counts

252 → 274

prune972.0ms (10.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	369	3	372
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	371	14	385

Error

2.9b

Counts

385 → 14

Alt Table

Status	Error	Program
	29.2b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (hypot.f64 b (sqrt.f64 (.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))))))
▶	18.1b	(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 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 2))))))
	18.2b	(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) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	32.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	21.9b	(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) (.f64 -1 b))))
	30.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	18.1b	(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) (.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)))))))))
	20.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.6b	(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 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	19.5b	(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))))))
	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) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))))))
	28.6b	(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 (neg.f64 b) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))))
✓	18.0b	(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))))))
	18.1b	(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 26991 to 17087 computations (36.7% saved)

localize59.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.6b	(+.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 2))))
	20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	20.7b	(sqrt.f64 (.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) 2)))
✓	21.4b	(cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series123.0ms (1.4%)

Counts

3 → 76

Calls

3 calls:

59.0ms

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

36.0ms

(+.f64 (neg.f64 b) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 2))))

29.0ms

(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 2)))

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

364×	`fma-def_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
143×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	318	40
2	3746	40

Stop Event

1×	node limit

Counts

3 → 95

Calls

3 calls:

51.0ms

(+.f64 (neg.f64 b) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 2))))

51.0ms

(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4)))) 2)))

51.0ms

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

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-def_binary64`
502×	`cancel-sign-sub-inv_binary64`
179×	`fma-neg_binary64`
177×	`unswap-sqr_binary64`
170×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	3233
1	789	3173
2	2910	3059

Stop Event

1×	node limit

Counts

171 → 188

prune823.0ms (9.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	306	14	320

Error

2.9b

Counts

320 → 14

Alt Table

Status	Error	Program
	29.2b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (hypot.f64 b (sqrt.f64 (.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))))))
✓	18.1b	(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 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 2))))))
	18.2b	(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) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	32.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	21.9b	(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) (.f64 -1 b))))
	30.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	18.1b	(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) (.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)))))))))
	20.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	21.6b	(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 (neg.f64 b) (fma.f64 2 (.f64 a (/.f64 c b)) (neg.f64 b)))))
	19.5b	(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))))))
	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) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))))))
	28.6b	(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 (neg.f64 b) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))))
✓	18.0b	(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))))))
▶	18.1b	(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 19435 to 12293 computations (36.7% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 b b (.f64 c (.f64 a -4)))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b)
✓	0.8b	(+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))
✓	20.7b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series143.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

67.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b)
37.0ms	(+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))
27.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))
11.0ms	(fma.f64 b b (.f64 c (.f64 a -4)))

rewrite72.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`fma-def_binary64`
274×	`fma-neg_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
207×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	240	53
2	3249	53

Stop Event

1×	node limit

Counts

4 → 207

Calls

4 calls:

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

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	2198
1	297	2110
2	967	2022

Stop Event

1×	node limit

Counts

303 → 280

prune695.0ms (7.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	361	4	365
Fresh	1	10	11
Picked	1	0	1
Done	1	1	2
Total	364	15	379

Error

2.9b

Counts

379 → 15

Alt Table

Status	Error	Program
	18.2b	(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) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4))))) 3))))
	18.1b	(if (>=.f64 b 0) (.f64 (+.f64 b (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2)) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) b))))
	29.2b	(if (>=.f64 b 0) (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (+.f64 b (hypot.f64 b (sqrt.f64 (.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))))))
✓	18.1b	(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 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))) 2))))))
	30.6b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) 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 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (/.f64 -1/2 a)) (.f64 c (/.f64 2 (-.f64 (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) 3) b))))
	32.1b	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	21.9b	(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) (.f64 -1 b))))
	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) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))))))))
	24.1b	(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 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 3/2)) b))))
	28.6b	(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 (neg.f64 b) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))))
	21.7b	(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 (-.f64 (.f64 (/.f64 c b) (.f64 a 2)) b) b))))
	18.1b	(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) (.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)))))))))
	20.2b	(if (>=.f64 b 0) (/.f64 (-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 b)) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	19.5b	(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 16430 to 10247 computations (37.6% saved)

regimes1.7s (18.8%)

Accuracy

Total 3.8b remaining (54.3%)

Threshold costs 0b (0%)

Counts

145 → 3

Compiler

Compiled 23502 to 15806 computations (32.7% saved)

bsearch68.0ms (0.8%)

Steps

Iters	Range		Point
8	1.6284574590265306e+66	1.6286430836551103e+69	1.0415532491463108e+69
6	-1.0269664041298781e+126	-1.2768023275738033e+114	-1.4362804565109957e+116

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`+-commutative_binary64`
18×	`*-commutative_binary64`
17×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	156
1	61	152
2	90	152
3	121	152
4	141	152
5	152	152
6	155	152

Stop Event

1×

saturated

end355.0ms (3.9%)

Compiler: Compiled 836 to 548 computations (34.4% saved)

Details

analyze758.0ms (8.4%)

sample1.8s (20.2%)

simplify37.0ms (0.4%)

prune5.0ms (0.1%)

localize21.0ms (0.2%)

series103.0ms (1.1%)

rewrite69.0ms (0.8%)

simplify51.0ms (0.6%)

prune668.0ms (7.4%)

localize28.0ms (0.3%)

series75.0ms (0.8%)

rewrite111.0ms (1.2%)

simplify58.0ms (0.6%)

prune972.0ms (10.8%)

localize59.0ms (0.7%)

series123.0ms (1.4%)

rewrite53.0ms (0.6%)

simplify64.0ms (0.7%)

prune823.0ms (9.1%)

localize37.0ms (0.4%)

series143.0ms (1.6%)

rewrite72.0ms (0.8%)

simplify49.0ms (0.5%)

prune695.0ms (7.7%)

regimes1.7s (18.8%)

bsearch68.0ms (0.8%)

simplify6.0ms (0.1%)

end355.0ms (3.9%)

Profiling