Details

analyze1.2s (19.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.3%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.7s (29.3%)

Results

1.3s	8254×	body	128	valid
373.0ms	2346×	body	128	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 46 to 32 computations (30.4% saved)

preprocess40.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

527×	`cancel-sign-sub-inv_binary64`
455×	`associate-+r+_binary64`
420×	`sub-neg_binary64`
388×	`+-commutative_binary64`
336×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	384
1	297	352
2	1178	352
3	3828	352
0	6	6
1	6	6

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
503×	`fma-def_binary64`
447×	`sub-neg_binary64`
362×	`unsub-neg_binary64`
320×	`+-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	106	22
3	334	21
4	1058	20
5	2896	20
6	4356	20

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y) (fma.f64 (+.f64 a -1/2) b x))
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 120 to 80 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 a 1/2) b)
✓	0.1b	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
✓	0.3b	(*.f64 z (log.f64 t))

series308.0ms (5.2%)

Counts

3 → 68

Calls

24 calls:

65.0ms	(*.f64 z (log.f64 t))	z	0
49.0ms	(*.f64 z (log.f64 t))	z	-inf
48.0ms	(*.f64 z (log.f64 t))	z	inf
14.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))	z	inf
13.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))	y	0

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

322×	`log1p-udef_binary64`
178×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	343	28
2	4951	28

Stop Event

1×	node limit

Counts

3 → 87

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

558×	`sub-neg_binary64`
433×	`fma-neg_binary64`
389×	`associate--r+_binary64`
270×	`fma-def_binary64`
243×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	790
1	116	790
2	260	676
3	619	676
4	1675	676
5	3867	676

Stop Event

1×	node limit

Counts

155 → 109

prune116.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (-.f64 (.f64 a b) (*.f64 1/2 b)))
	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y) (fma.f64 (+.f64 a -1/2) b x))
	30.2b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 2) (.f64 (-.f64 a 1/2) b))
	1.0b	(+.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 3) (.f64 (-.f64 a 1/2) b))
	35.8b	(+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x y) 2) (.f64 (.f64 z (-.f64 1 (log.f64 t))) (.f64 z (-.f64 1 (log.f64 t))))) (-.f64 (+.f64 x y) (.f64 z (-.f64 1 (log.f64 t))))) (*.f64 (-.f64 a 1/2) b))
▶	0.1b	(+.f64 (+.f64 z (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (.f64 (-.f64 a 1/2) b))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (cbrt.f64 (.f64 z (log.f64 t))) 3)) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 2706 to 1264 computations (53.3% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 a 1/2) b)
✓	0.1b	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))
	0.3b	(*.f64 z (log.f64 t))

series115.0ms (1.9%)

Counts

1 → 48

Calls

12 calls:

13.0ms	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))	x	0
12.0ms	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))	y	inf
11.0ms	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))	z	inf
11.0ms	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))	z	-inf
11.0ms	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))	y	0

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`fma-def_binary64`
338×	`fma-neg_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
122×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	232	15
2	3566	15

Stop Event

1×	node limit

Counts

1 → 68

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
551×	`unsub-neg_binary64`
355×	`sub-neg_binary64`
268×	`fma-neg_binary64`
210×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	635
1	88	635
2	201	553
3	512	553
4	1243	553
5	3063	553
6	4481	553

Stop Event

1×	node limit

Counts

116 → 82

prune160.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	124	7	131

Error

0.0b

Counts

131 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 z (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (+.f64 (.f64 b a) (*.f64 b -1/2)))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (cbrt.f64 (.f64 z (log.f64 t))) 3)) (.f64 (-.f64 a 1/2) b))
	30.2b	(+.f64 (fma.f64 (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) z) (*.f64 (-.f64 a 1/2) b))
	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y) (fma.f64 (+.f64 a -1/2) b x))
	30.2b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 2) (.f64 (-.f64 a 1/2) b))
	1.0b	(+.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 3) (.f64 (-.f64 a 1/2) b))
	35.8b	(+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x y) 2) (.f64 (.f64 z (-.f64 1 (log.f64 t))) (.f64 z (-.f64 1 (log.f64 t))))) (-.f64 (+.f64 x y) (.f64 z (-.f64 1 (log.f64 t))))) (*.f64 (-.f64 a 1/2) b))

Compiler

Compiled 3085 to 1223 computations (60.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 b a) (.f64 b -1/2))
	0.1b	(+.f64 z (-.f64 (+.f64 x y) (*.f64 z (log.f64 t))))
	0.3b	(*.f64 z (log.f64 t))

series5.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(+.f64 (.f64 b a) (.f64 b -1/2))	b	-inf
1.0ms	(+.f64 (.f64 b a) (.f64 b -1/2))	b	inf
1.0ms	(+.f64 (.f64 b a) (.f64 b -1/2))	b	0
1.0ms	(+.f64 (.f64 b a) (.f64 b -1/2))	a	-inf
1.0ms	(+.f64 (.f64 b a) (.f64 b -1/2))	a	0

rewrite42.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`log1p-expm1-u_binary64`
758×	`expm1-log1p-u_binary64`
139×	`log1p-udef_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	153	7
2	2042	7

Stop Event

1×	node limit

Counts

1 → 43

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

101×	`fma-def_binary64`
78×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
18×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	159
1	32	159
2	66	159
3	138	159
4	240	159
5	367	159
6	509	159
7	548	159

Stop Event

1×

saturated

Counts

67 → 49

prune154.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	147	7	154

Error

0.0b

Counts

154 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 z (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (+.f64 (.f64 b a) (*.f64 b -1/2)))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (cbrt.f64 (.f64 z (log.f64 t))) 3)) (.f64 (-.f64 a 1/2) b))
	30.2b	(+.f64 (fma.f64 (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) z) (*.f64 (-.f64 a 1/2) b))
▶	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y) (fma.f64 (+.f64 a -1/2) b x))
	30.2b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 2) (.f64 (-.f64 a 1/2) b))
	1.0b	(+.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 y (.f64 z (-.f64 1 (log.f64 t)))))) 3) (.f64 (-.f64 a 1/2) b))
	35.8b	(+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x y) 2) (.f64 (.f64 z (-.f64 1 (log.f64 t))) (.f64 z (-.f64 1 (log.f64 t))))) (-.f64 (+.f64 x y) (.f64 z (-.f64 1 (log.f64 t))))) (*.f64 (-.f64 a 1/2) b))

Compiler

Compiled 3879 to 1441 computations (62.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 t))
✓	0.0b	(fma.f64 (+.f64 a -1/2) b x)
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) y)

series111.0ms (1.9%)

Counts

3 → 80

Calls

21 calls:

12.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) y)	z	0
11.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) y)	y	0
11.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) y)	z	-inf
11.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) y)	z	inf
10.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) y)	y	inf

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

332×	`prod-diff_binary64`
261×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
146×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	289	24
2	3511	24

Stop Event

1×	node limit

Counts

3 → 76

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-neg_binary64`
570×	`fma-def_binary64`
474×	`unsub-neg_binary64`
261×	`distribute-rgt-in_binary64`
241×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	774
1	119	747
2	249	658
3	558	631
4	1188	631
5	2633	631
6	4911	631

Stop Event

1×	node limit

Counts

156 → 99

prune124.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Status	Error	Program
	30.2b	(+.f64 (fma.f64 (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) z) (*.f64 (-.f64 a 1/2) b))
	0.7b	(+.f64 (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y)) 3) (fma.f64 (+.f64 a -1/2) b x))
✓	0.1b	(+.f64 (+.f64 z (-.f64 (+.f64 x y) (.f64 z (log.f64 t)))) (+.f64 (.f64 b a) (*.f64 b -1/2)))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (pow.f64 (cbrt.f64 (.f64 z (log.f64 t))) 3)) (.f64 (-.f64 a 1/2) b))
✓	0.1b	(+.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y) (fma.f64 (+.f64 a -1/2) b x))
	0.1b	(+.f64 (fma.f64 z (*.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (/.f64 1 (+.f64 1 (fma.f64 (log.f64 t) (log.f64 t) (log.f64 t))))) y) (fma.f64 (+.f64 a -1/2) b x))
	0.2b	(+.f64 (fma.f64 z (*.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 2))) y) (fma.f64 (+.f64 a -1/2) b x))
	18.4b	(+.f64 (pow.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) y)) 2) (fma.f64 (+.f64 a -1/2) b x))

Compiler

Compiled 2038 to 1162 computations (43% saved)

regimes1.2s (20.9%)

Accuracy

Total 0.1b remaining (77.3%)

Threshold costs 0.1b (77.3%)

Counts

97 → 1

Compiler

Compiled 28107 to 19711 computations (29.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	26	25
2	38	25
3	44	25
4	48	25
5	49	25

Stop Event

1×

saturated

end153.0ms (2.6%)

Stop Event

1×

fuel

Remove

(sort x y)

Compiler

Compiled 302 to 201 computations (33.4% saved)

Details

analyze1.2s (19.9%)

sample1.7s (29.3%)

preprocess40.0ms (0.7%)

simplify32.0ms (0.5%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

series308.0ms (5.2%)

rewrite68.0ms (1.1%)

simplify48.0ms (0.8%)

prune116.0ms (2%)

localize13.0ms (0.2%)

series115.0ms (1.9%)

rewrite53.0ms (0.9%)

simplify48.0ms (0.8%)

prune160.0ms (2.7%)

localize13.0ms (0.2%)

series5.0ms (0.1%)

rewrite42.0ms (0.7%)

simplify17.0ms (0.3%)

prune154.0ms (2.6%)

localize11.0ms (0.2%)

series111.0ms (1.9%)

rewrite58.0ms (1%)

simplify57.0ms (1%)

prune124.0ms (2.1%)

regimes1.2s (20.9%)

simplify4.0ms (0.1%)

end153.0ms (2.6%)

Profiling