Details

analyze715.0ms (10%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.0s (27.6%)

Results

631.0ms	5363×	body	128	valid
496.0ms	1103×	body	2048	valid
287.0ms	779×	body	1024	valid
227.0ms	418×	body	4096	valid
125.0ms	1089×	body	128	invalid
105.0ms	382×	body	512	valid
42.0ms	211×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
208×	`associate-/l*_binary64`
205×	`fma-def_binary64`
181×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	57	20
3	126	20
4	216	20
5	392	20
6	662	20
7	1008	20
8	1214	20
9	1599	20
10	3126	20
11	3899	20
12	3997	20
13	4005	20
14	4013	20
15	4013	20
16	4071	20
17	4107	20
18	4137	20
19	4149	20

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

35.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.3b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.4b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series189.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
68.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
32.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite74.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

352×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
192×	`egg-rr`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	262	55
2	4018	55

Stop Event

1×	node limit

Counts

4 → 192

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
70.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
70.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
70.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
496×	`associate-/l*_binary64`
402×	`associate-/r*_binary64`
369×	`fma-def_binary64`
143×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	2047
1	409	2003
2	1439	1977

Stop Event

1×	node limit

Counts

288 → 269

prune191.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	259	10	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	10	270

Error

4.9b

Counts

270 → 10

Alt Table

Status	Error	Program
	37.3b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
▶	35.3b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	46.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	38.9b	(/.f64 -1/2 (/.f64 b_2 c))
	51.3b	(fma.f64 (/.f64 -1 (sqrt.f64 a)) (/.f64 b_2 (sqrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	38.8b	(*.f64 -1/2 (/.f64 c b_2))
	55.9b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	45.4b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))
	45.3b	(*.f64 (/.f64 -2 a) b_2)
	46.9b	(/.f64 (/.f64 (neg.f64 (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c))) (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)

Compiler

Compiled 6122 to 2034 computations (66.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.4b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series93.0ms (1.3%)

Counts

2 → 40

Calls

2 calls:

62.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
31.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`fma-neg_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	292	29
2	4222	29

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

51.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
51.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

692×	`times-frac_binary64`
458×	`associate-/l*_binary64`
372×	`associate-/r*_binary64`
314×	`associate-l_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1176
1	322	1144
2	1138	1130

Stop Event

1×	node limit

Counts

122 → 130

prune141.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	250	12	262

Error

4.9b

Counts

262 → 12

Alt Table

Status	Error	Program
▶	37.3b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
✓	35.3b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	46.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	38.9b	(/.f64 -1/2 (/.f64 b_2 c))
	46.9b	(/.f64 (/.f64 (neg.f64 (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c))) (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	41.9b	(.f64 (+.f64 b_2 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)) 3/2))) (/.f64 1 (neg.f64 a)))
	56.1b	(.f64 (+.f64 b_2 (-.f64 (.f64 1/2 (/.f64 a (/.f64 b_2 c))) b_2)) (/.f64 1 (neg.f64 a)))
	45.2b	(*.f64 -2 (/.f64 b_2 a))
	51.3b	(fma.f64 (/.f64 -1 (sqrt.f64 a)) (/.f64 b_2 (sqrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	38.8b	(*.f64 -1/2 (/.f64 c b_2))
	55.9b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	45.4b	(fma.f64 (/.f64 b_2 a) -2 (*.f64 1/2 (/.f64 c b_2)))

Compiler

Compiled 6208 to 2434 computations (60.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 a)
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	22.4b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series122.0ms (1.7%)

Counts

2 → 34

Calls

2 calls:

73.0ms	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
49.0ms	(cbrt.f64 a)

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

299×	`log1p-udef_binary64`
181×	`add-sqr-sqrt_binary64`
172×	`add-cbrt-cube_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	376	26
2	4971	26

Stop Event

1×	node limit

Counts

2 → 48

Calls

2 calls:

56.0ms	(cbrt.f64 a)
56.0ms	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
355×	`unswap-sqr_binary64`
242×	`associate-/l*_binary64`
224×	`associate-r_binary64`
209×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	669
1	237	647
2	766	641
3	4082	641

Stop Event

1×	node limit

Counts

82 → 77

prune132.0ms (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	224	13	237

Error

4.9b

Counts

237 → 13

Alt Table

Status	Error	Program
	45.5b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 b_2 a)))
✓	37.3b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
✓	35.3b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	46.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	38.9b	(/.f64 -1/2 (/.f64 b_2 c))
	61.4b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (neg.f64 b_2) a)))
▶	38.8b	(*.f64 -1/2 (/.f64 c b_2))
	46.9b	(/.f64 (/.f64 (neg.f64 (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c))) (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	41.9b	(.f64 (+.f64 b_2 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)) 3/2))) (/.f64 1 (neg.f64 a)))
	56.1b	(.f64 (+.f64 b_2 (-.f64 (.f64 1/2 (/.f64 a (/.f64 b_2 c))) b_2)) (/.f64 1 (neg.f64 a)))
	45.2b	(*.f64 -2 (/.f64 b_2 a))
	51.3b	(fma.f64 (/.f64 -1 (sqrt.f64 a)) (/.f64 b_2 (sqrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	45.4b	(fma.f64 (/.f64 b_2 a) -2 (*.f64 1/2 (/.f64 c b_2)))

Compiler

Compiled 6611 to 2544 computations (61.5% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (/.f64 c b_2))

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

7.0ms

(*.f64 -1/2 (/.f64 c b_2))

rewrite33.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
317×	`log-prod_binary64`
116×	`expm1-udef_binary64`
116×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1622	7

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

33.0ms

(*.f64 -1/2 (/.f64 c b_2))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

prune22.0ms (0.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	24	14	38

Error

4.9b

Counts

38 → 14

Alt Table

Status	Error	Program
	45.5b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 b_2 a)))
✓	37.3b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
✓	35.3b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 a)))
	61.4b	(fma.f64 (/.f64 -1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 b_2 (cbrt.f64 a)) (neg.f64 (/.f64 (neg.f64 b_2) a)))
✓	38.8b	(*.f64 -1/2 (/.f64 c b_2))
	47.0b	(exp.f64 (log.f64 (/.f64 (*.f64 -1/2 c) b_2)))
	46.9b	(/.f64 (/.f64 (neg.f64 (+.f64 (fma.f64 b_2 b_2 (.f64 b_2 b_2)) (.f64 a c))) (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	41.9b	(.f64 (+.f64 b_2 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)) 3/2))) (/.f64 1 (neg.f64 a)))
	51.3b	(fma.f64 (/.f64 -1 (sqrt.f64 a)) (/.f64 b_2 (sqrt.f64 a)) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	46.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 2) (.f64 (cbrt.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (/.f64 1 a)))
	55.4b	(log.f64 (pow.f64 (exp.f64 -1/2) (/.f64 c b_2)))
	39.2b	(/.f64 (/.f64 (*.f64 -1/2 c) (pow.f64 (cbrt.f64 b_2) 2)) (cbrt.f64 b_2))
	45.4b	(fma.f64 (/.f64 b_2 a) -2 (*.f64 1/2 (/.f64 c b_2)))
	45.2b	(*.f64 -2 (/.f64 b_2 a))

Compiler

Compiled 465 to 308 computations (33.8% saved)

regimes2.9s (40.7%)

Accuracy

Total 4.9b remaining (45.5%)

Threshold costs 0b (0%)

Counts

182 → 3

Compiler

Compiled 14092 to 8874 computations (37% saved)

bsearch25.0ms (0.3%)

Steps

Iters	Range		Point
1	2.5810664223351267e+72	1.4282150786340163e+85	6.1115744018599626e+78
3	-8.204753307206658e-44	-6.543761883102639e-44	-6.647573847109141e-44

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`*-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	56
1	45	56
2	66	56
3	83	56
4	92	56
5	95	56

Stop Event

1×

saturated

end177.0ms (2.5%)

Compiler: Compiled 327 to 206 computations (37% saved)

Details

analyze715.0ms (10%)

sample2.0s (27.6%)

simplify62.0ms (0.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series189.0ms (2.6%)

rewrite74.0ms (1%)

simplify46.0ms (0.6%)

prune191.0ms (2.7%)

localize9.0ms (0.1%)

series93.0ms (1.3%)

rewrite53.0ms (0.7%)

simplify33.0ms (0.5%)

prune141.0ms (2%)

localize15.0ms (0.2%)

series122.0ms (1.7%)

rewrite57.0ms (0.8%)

simplify40.0ms (0.6%)

prune132.0ms (1.9%)

localize3.0ms (0%)

series7.0ms (0.1%)

rewrite33.0ms (0.5%)

simplify6.0ms (0.1%)

prune22.0ms (0.3%)

regimes2.9s (40.7%)

bsearch25.0ms (0.3%)

simplify4.0ms (0%)

end177.0ms (2.5%)

Profiling