Details

analyze701.0ms (14.6%)

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)

sample1.9s (39.6%)

Results

621.0ms	5391×	body	128	valid
504.0ms	1134×	body	2048	valid
269.0ms	749×	body	1024	valid
216.0ms	399×	body	4096	valid
123.0ms	1076×	body	128	invalid
119.0ms	410×	body	512	valid
34.0ms	173×	body	256	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess34.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

869×	`fma-neg_binary64`
440×	`times-frac_binary64`
394×	`fma-def_binary64`
350×	`cancel-sign-sub-inv_binary64`
345×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	82	80
2	167	80
3	390	80
4	694	80
5	1249	80
6	3263	80
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify115.0ms (2.4%)

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

37.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.1b	(/.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 (0.2%)

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)
✓	0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series128.0ms (2.7%)

Counts

4 → 96

Calls

36 calls:

22.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))	c	-inf
9.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)	a	inf
9.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)	a	-inf
7.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)	c	-inf
7.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)	c	inf

rewrite72.0ms (1.5%)

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

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
496×	`associate-/l*_binary64`
400×	`associate-/r*_binary64`
370×	`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 → 268

prune149.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	257	11	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	11	269

Error

5.1b

Counts

269 → 11

Alt Table

Status	Error	Program
	47.8b	(*.f64 (/.f64 -2 a) b_2)
	37.2b	(fma.f64 -1 (/.f64 b_2 a) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	38.1b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) 3)) a)
	47.1b	(/.f64 (fma.f64 (sqrt.f64 b_2) (neg.f64 (sqrt.f64 b_2)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	39.8b	(/.f64 (*.f64 (/.f64 a (/.f64 b_2 c)) -1/2) a)
	46.5b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	47.7b	(/.f64 (*.f64 -2 b_2) a)
	46.8b	(/.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)
▶	36.4b	(*.f64 -1/2 (/.f64 c b_2))
	55.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	47.8b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))

Compiler

Compiled 6095 to 2037 computations (66.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

1.0ms	(*.f64 -1/2 (/.f64 c b_2))	c	0
1.0ms	(*.f64 -1/2 (/.f64 c b_2))	c	inf
1.0ms	(*.f64 -1/2 (/.f64 c b_2))	c	-inf
1.0ms	(*.f64 -1/2 (/.f64 c b_2))	b_2	-inf
1.0ms	(*.f64 -1/2 (/.f64 c b_2))	b_2	inf

rewrite34.0ms (0.7%)

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

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

prune32.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	24	12	36

Error

5.1b

Counts

36 → 12

Alt Table

Status	Error	Program
	47.8b	(*.f64 (/.f64 -2 a) b_2)
	37.2b	(fma.f64 -1 (/.f64 b_2 a) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	38.1b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) 3)) a)
	47.1b	(/.f64 (fma.f64 (sqrt.f64 b_2) (neg.f64 (sqrt.f64 b_2)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	47.4b	(exp.f64 (log.f64 (/.f64 (*.f64 -1/2 c) b_2)))
	46.5b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	47.7b	(/.f64 (*.f64 -2 b_2) a)
	36.8b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)
	46.8b	(/.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)
▶	36.4b	(/.f64 (*.f64 -1/2 c) b_2)
	55.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	47.8b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))

Compiler

Compiled 562 to 376 computations (33.1% saved)

localize3.0ms (0.1%)

prune12.0ms (0.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	11	11
Picked	1	1
Done	0	0
Total	12	12

Error

5.1b

Counts

12 → 12

Alt Table

Status	Error	Program
	47.8b	(*.f64 (/.f64 -2 a) b_2)
	37.2b	(fma.f64 -1 (/.f64 b_2 a) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	38.1b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) 3)) a)
	47.1b	(/.f64 (fma.f64 (sqrt.f64 b_2) (neg.f64 (sqrt.f64 b_2)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	47.4b	(exp.f64 (log.f64 (/.f64 (*.f64 -1/2 c) b_2)))
	46.5b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	47.7b	(/.f64 (*.f64 -2 b_2) a)
▶	36.8b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)
	46.8b	(/.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)
✓	36.4b	(/.f64 (*.f64 -1/2 c) b_2)
	55.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	47.8b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))

Compiler

Compiled 334 to 218 computations (34.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)
✓	16.2b	(cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2))

series141.0ms (2.9%)

Counts

2 → 0

Calls

12 calls:

22.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)	c	inf
21.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)	b_2	0
21.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)	c	0
20.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2)) 3)	b_2	inf
12.0ms	(cbrt.f64 (/.f64 (*.f64 -1/2 c) b_2))	c	inf

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`log1p-expm1-u_binary64`
812×	`expm1-log1p-u_binary64`
91×	`egg-rr`
83×	`add-sqr-sqrt_binary64`
79×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	189	16
2	2207	16

Stop Event

1×	node limit

Counts

2 → 91

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

91 → 91

prune53.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	90	13	103

Error

5.1b

Counts

103 → 13

Alt Table

Status	Error	Program
	47.8b	(*.f64 (/.f64 -2 a) b_2)
	37.2b	(fma.f64 -1 (/.f64 b_2 a) (neg.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)))
	47.5b	(pow.f64 (exp.f64 (.f64 (log.f64 (.f64 -1/2 (/.f64 c b_2))) 1/3)) 3)
	38.1b	(/.f64 (-.f64 (neg.f64 b_2) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) 3)) a)
	47.1b	(/.f64 (fma.f64 (sqrt.f64 b_2) (neg.f64 (sqrt.f64 b_2)) (neg.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	47.5b	(pow.f64 (pow.f64 (pow.f64 (*.f64 -1/2 (/.f64 c b_2)) 1/6) 2) 3)
	47.7b	(/.f64 (*.f64 -2 b_2) a)
	46.5b	(.f64 (-.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	46.8b	(/.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)
	38.1b	(pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 -1/2 (/.f64 c b_2)))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 c b_2))) 2) 1/3)) 3)
✓	36.4b	(/.f64 (*.f64 -1/2 c) b_2)
	55.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	47.8b	(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))

Compiler

Compiled 1238 to 829 computations (33% saved)

regimes1.1s (21.8%)

Accuracy

Total 4.5b remaining (44.5%)

Threshold costs 0b (0%)

Counts

66 → 3

Compiler

Compiled 4664 to 2994 computations (35.8% saved)

bsearch70.0ms (1.5%)

Algorithm

2×	binary-search

Calls

2 calls:

46.0ms	b_2
22.0ms	b_2

Steps

Iters	Point		Range
1.1253871947171223e+114	∈ [	5.214570015592262e+110	,	1.6176298619418202e+115	]
-6.800448154136341e-99	∈ [	-1.8672352006382376e-98	,	-2.170351639190422e-105	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	59
1	49	59
2	71	59
3	86	59
4	96	59
5	100	59
6	101	59

Stop Event

1×

saturated

end161.0ms (3.3%)

Stop Event

1×

fuel

Compiler

Compiled 287 to 191 computations (33.4% saved)

Details

analyze701.0ms (14.6%)

sample1.9s (39.6%)

preprocess34.0ms (0.7%)

simplify115.0ms (2.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series128.0ms (2.7%)

rewrite72.0ms (1.5%)

simplify63.0ms (1.3%)

prune149.0ms (3.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite34.0ms (0.7%)

simplify6.0ms (0.1%)

prune32.0ms (0.7%)

localize3.0ms (0.1%)

prune12.0ms (0.3%)

localize5.0ms (0.1%)

series141.0ms (2.9%)

rewrite42.0ms (0.9%)

simplify6.0ms (0.1%)

prune53.0ms (1.1%)

regimes1.1s (21.8%)

bsearch70.0ms (1.5%)

simplify6.0ms (0.1%)

end161.0ms (3.3%)

Profiling