Details

analyze627.0ms (4.7%)

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
34.3%	65.5%	0.1%	6
37.4%	56.2%	6.4%	7
44.5%	49.1%	6.4%	8
51.1%	40.2%	8.7%	9
54.2%	32.4%	13.4%	10
59.3%	26.5%	14.2%	11
62.7%	20.8%	16.5%	12
64.4%	16.7%	19%	13
67.1%	13.5%	19.4%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample2.1s (15.5%)

Results

1.8s	8256×	body	128	valid
140.0ms	666×	body	128	invalid

Compiler

Compiled 125 to 80 computations (36% saved)

simplify176.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1753×	`fma-neg_binary64`
1288×	`fma-def_binary64`
631×	`div-sub_binary64`
512×	`times-frac_binary64`
430×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	47	52
2	118	52
3	269	50
4	429	50
5	743	50
6	1315	50
7	1738	50
8	2176	50
9	2853	50
10	4066	50
11	3523	50
12	3575	50
13	3543	50
14	3557	50
15	4510	50
16	4622	50
17	4761	50

prune7.0ms (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

17.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	17.3b	(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 (.f64 b b) (.f64 (.f64 4 a) c))))))

Status

Error

Program

▶

17.2b

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

17.3b

(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 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

Compiler

Compiled 231 to 143 computations (38.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	25.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series509.0ms (3.8%)

Counts

4 → 80

Calls

4 calls:

323.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
80.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
55.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
51.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify238.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-neg-in_binary64`
159×	`distribute-rgt-in_binary64`
157×	`distribute-lft-neg-in_binary64`

Counts

186 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	5384
1	686	4516
2	2546	4321
3	4500	4319
4	4865	4319

prune870.0ms (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	267	11	278
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	269	11	280

Error

4.8b

Counts

280 → 11

Alt Table

Status	Error	Program
	19.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	17.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
▶	17.2b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	21.7b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	21.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 13561 to 7937 computations (41.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	11.5b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
	25.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series120.0ms (0.9%)

Counts

2 → 40

Calls

2 calls:

71.0ms

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

49.0ms

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

rewrite65.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
63×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
25×	`pow1_binary64`
16×	`rem-sqrt-square_binary64`

Counts

2 → 106

Calls

2 calls:

19.0ms

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

18.0ms

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

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
520×	`fma-neg_binary64`
492×	`associate-/l*_binary64`
466×	`associate-/r*_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

146 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3334
1	433	3107
2	1519	2864
3	4924	2864
4	5070	2864

prune942.0ms (7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	337	10	347

Error

4.8b

Counts

347 → 10

Alt Table

Status	Error	Program
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
▶	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	19.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	17.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	21.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 18836 to 11225 computations (40.4% saved)

localize48.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 c 2) (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b))
	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
	11.5b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
	25.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series561.0ms (4.2%)

Counts

1 → 20

Calls

1 calls:

561.0ms

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

12.0ms

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

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

799×	`times-frac_binary64`
671×	`associate-/l*_binary64`
369×	`associate-/r*_binary64`
224×	`associate-/l/_binary64`
215×	`fma-def_binary64`

Counts

47 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1469
1	373	1298
2	1260	1230
3	4931	1230
4	5005	1230

prune938.0ms (7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	360	10	370

Error

4.8b

Counts

370 → 10

Alt Table

Status	Error	Program
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	19.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
▶	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	17.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	21.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 21003 to 11845 computations (43.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	1.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.8b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series293.0ms (2.2%)

Counts

1 → 20

Calls

1 calls:

293.0ms

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

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
48×	`sqrt-prod_binary64`
45×	`*-un-lft-identity_binary64`
33×	`associate-r_binary64`

Counts

1 → 97

Calls

1 calls:

27.0ms

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

simplify233.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

817×	`times-frac_binary64`
412×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
286×	`fma-def_binary64`
227×	`associate-/r/_binary64`

Counts

117 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	5862
1	639	4887
2	1962	4516
3	4996	4516

prune2.2s (16.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	476	0	476
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	476	10	486

Error

4.8b

Counts

486 → 10

Alt Table

Status	Error	Program
	17.8b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (*.f64 -1 b) b)))
✓	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (sqrt.f64 b) (sqrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)))
	19.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b b) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
✓	17.3b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (/.f64 2 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))))
	17.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (.f64 c 2))))
	21.4b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (/.f64 (.f64 c 2) (-.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b)))
	21.9b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	22.0b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	33.6b	(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (/.f64 (neg.f64 (+.f64 (.f64 a (.f64 c -4)) 0)) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 29247 to 16993 computations (41.9% saved)

regimes2.6s (19.7%)

Accuracy

Total 0.9b remaining (14.5%)

Threshold costs 0.9b (14.5%)

Counts

153 → 3

Compiler

Compiled 26586 to 17158 computations (35.5% saved)

bsearch53.0ms (0.4%)

Steps

Iters	Range		Point
5	4.199021549675812e+120	1.1422987145425663e+124	1.2286315327439822e+123
1	-2.2335073275075362e+107	-4.48799788613306e+105	-3.1911412341454343e+106

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	148
1	67	146
2	90	146
3	109	146
4	122	146
5	128	146
6	129	146
7	128	146

end489.0ms (3.6%)

Compiler: Compiled 626 to 393 computations (37.2% saved)

Details

analyze627.0ms (4.7%)

sample2.1s (15.5%)

simplify176.0ms (1.3%)

prune7.0ms (0%)

localize30.0ms (0.2%)

series509.0ms (3.8%)

rewrite23.0ms (0.2%)

simplify238.0ms (1.8%)

prune870.0ms (6.5%)

localize23.0ms (0.2%)

series120.0ms (0.9%)

rewrite65.0ms (0.5%)

simplify127.0ms (0.9%)

prune942.0ms (7%)

localize48.0ms (0.4%)

series561.0ms (4.2%)

rewrite15.0ms (0.1%)

simplify77.0ms (0.6%)

prune938.0ms (7%)

localize21.0ms (0.2%)

series293.0ms (2.2%)

rewrite53.0ms (0.4%)

simplify233.0ms (1.7%)

prune2.2s (16.1%)

regimes2.6s (19.7%)

bsearch53.0ms (0.4%)

simplify8.0ms (0.1%)

end489.0ms (3.6%)

Profiling