Details

analyze680.0ms (7.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.5s (27.4%)

Results

738.0ms	5296×	body	128	valid
671.0ms	1206×	body	2048	valid
342.0ms	743×	body	1024	valid
312.0ms	439×	body	4096	valid
147.0ms	1043×	body	128	invalid
125.0ms	380×	body	512	valid
51.0ms	192×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify382.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune4.0ms (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

33.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	33.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize13.0ms (0.1%)

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 4 (.f64 a c))))) (.f64 2 a))
✓	0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series197.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

83.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
59.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
8.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify135.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-neg-in_binary64`
150×	`distribute-rgt-neg-out_binary64`
146×	`associate-r_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4202
1	693	3825
2	2488	3724
3	4652	3704
4	4985	3704

prune159.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	199	8	207
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Error

3.3b

Counts

209 → 9

Alt Table

Status	Error	Program
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	44.2b	(/.f64 (neg.f64 b) a)
	38.4b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) 2)))
	53.2b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))
▶	29.7b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))
	37.6b	(neg.f64 (/.f64 c b))
	35.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	30.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) 2) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a))

Compiler

Compiled 5667 to 3178 computations (43.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a))
✓	0.1b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))
✓	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
✓	12.9b	(sqrt.f64 (.f64 c (.f64 a -4)))

series834.0ms (9.2%)

Counts

4 → 36

Calls

4 calls:

425.0ms	(/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a))
240.0ms	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))
149.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
19.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite111.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

711×	`times-frac_binary64`
417×	`*-un-lft-identity_binary64`
417×	`add-sqr-sqrt_binary64`
319×	`add-cube-cbrt_binary64`
81×	`associate-/r*_binary64`

Counts

4 → 418

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))
11.0ms	(/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a))
7.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)

simplify540.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
357×	`associate-/r/_binary64`
258×	`*-commutative_binary64`
233×	`associate-/r*_binary64`
233×	`fma-neg_binary64`

Counts

454 → 637

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	18215
1	1135	16821
2	4086	16796
3	4950	16796
4	4945	16796

prune665.0ms (7.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	631	6	637
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	634	12	646

Error

1.4b

Counts

646 → 12

Alt Table

Status	Error	Program
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a)))
	44.6b	(/.f64 1 (fma.f64 -1 (/.f64 (.f64 a b) (.f64 c a)) (/.f64 a b)))
	53.2b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))
▶	29.6b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
	29.9b	(.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b) (sqrt.f64 2)) (/.f64 1 (.f64 a (sqrt.f64 2))))
	37.6b	(neg.f64 (/.f64 c b))
	30.2b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 a))))
	35.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	46.2b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b) b) a)))
	44.2b	(/.f64 (neg.f64 b) a)
✓	29.7b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))

Compiler

Compiled 22051 to 14748 computations (33.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 c a))
✓	0.1b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
✓	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)
✓	12.9b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series411.0ms (4.5%)

Counts

4 → 24

Calls

4 calls:

238.0ms	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
148.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)
20.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
5.0ms	(.f64 -4 (.f64 c a))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 89

Calls

4 calls:

7.0ms	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
4.0ms	(.f64 -4 (.f64 c a))
3.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
312×	`fma-neg_binary64`
270×	`cancel-sign-sub-inv_binary64`
260×	`neg-mul-1_binary64`
180×	`distribute-rgt-neg-in_binary64`

Counts

113 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	2916
1	616	2297
2	2276	2195
3	4533	2195
4	4943	2195

prune120.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	146	12	158

Error

1.4b

Counts

158 → 12

Alt Table

Status	Error	Program
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	29.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a)))
	44.6b	(/.f64 1 (fma.f64 -1 (/.f64 (.f64 a b) (.f64 c a)) (/.f64 a b)))
	53.2b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))
✓	29.6b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
	29.9b	(.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b) (sqrt.f64 2)) (/.f64 1 (.f64 a (sqrt.f64 2))))
	37.6b	(neg.f64 (/.f64 c b))
	30.2b	(/.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 a))))
	35.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	46.2b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b) b) a)))
	44.2b	(/.f64 (neg.f64 b) a)
✓	29.7b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))

Compiler

Compiled 4196 to 2505 computations (40.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)
	12.9b	(sqrt.f64 (.f64 c (.f64 a -4)))
	12.9b	(sqrt.f64 (.f64 -4 (.f64 c a)))

prune161.0ms (1.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	153	12	165

Error

1.4b

Counts

165 → 12

Alt Table

Status	Error	Program
	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	29.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a)))
	44.6b	(/.f64 1 (fma.f64 -1 (/.f64 (.f64 a b) (.f64 c a)) (/.f64 a b)))
	53.2b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))
✓	29.6b	(/.f64 (.f64 1/2 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b)) a)
✓	29.7b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) a)))
	30.7b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b)) (/.f64 2 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 c (.f64 a -4))))) b) b)) a)))
	29.9b	(.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b) b) (sqrt.f64 2)) (/.f64 1 (.f64 a (sqrt.f64 2))))
	37.6b	(neg.f64 (/.f64 c b))
	46.2b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b) b) a)))
	44.2b	(/.f64 (neg.f64 b) a)
	35.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))

Compiler

Compiled 6319 to 3909 computations (38.1% saved)

regimes1.7s (19.1%)

Accuracy

Total 7.8b remaining (74.5%)

Threshold costs 0b (0%)

Counts

142 → 3

Compiler

Compiled 13636 to 9677 computations (29% saved)

bsearch98.0ms (1.1%)

Steps

Iters	Range		Point
10	6.262670302237526e-14	6.277611502153688	2.0271929275340676e-10
9	-2.721120816297128e+161	-2.6206363159408652e+153	-3.274807826339219e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	39	50
2	46	50
3	50	50
4	51	50
5	51	50

end178.0ms (2%)

Compiler: Compiled 318 to 223 computations (29.9% saved)

Details

analyze680.0ms (7.5%)

sample2.5s (27.4%)

simplify382.0ms (4.2%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series197.0ms (2.2%)

rewrite29.0ms (0.3%)

simplify135.0ms (1.5%)

prune159.0ms (1.7%)

localize12.0ms (0.1%)

series834.0ms (9.2%)

rewrite111.0ms (1.2%)

simplify540.0ms (5.9%)

prune665.0ms (7.3%)

localize9.0ms (0.1%)

series411.0ms (4.5%)

rewrite21.0ms (0.2%)

simplify93.0ms (1%)

prune120.0ms (1.3%)

localize18.0ms (0.2%)

prune161.0ms (1.8%)

regimes1.7s (19.1%)

bsearch98.0ms (1.1%)

simplify4.0ms (0%)

end178.0ms (2%)

Profiling