Details

analyze1.6s (21.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.7s (22.4%)

Results

1.1s	8256×	body	128	valid
500.0ms	3339×	body	128	invalid

Compiler

Compiled 38 to 28 computations (26.3% saved)

preprocess46.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

770×	`times-frac_binary64`
393×	`distribute-neg-frac_binary64`
388×	`associate-/r/_binary64`
376×	`fma-def_binary64`
338×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	209
1	199	187
2	704	187
3	2404	187
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
757×	`fma-neg_binary64`
385×	`associate-/l*_binary64`
290×	`associate-/r/_binary64`
265×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	31	17
2	109	17
3	349	17
4	992	17
5	2393	17
6	4046	17
7	4848	17

Stop Event

1×	node limit

Counts

1 → 2

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

7.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.0b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)
	7.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 100 to 70 computations (30% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2)))
✓	6.6b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)

series51.0ms (0.7%)

Counts

2 → 108

Calls

27 calls:

5.0ms	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)	y	inf
3.0ms	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)	a	-inf
2.0ms	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)	a	inf
2.0ms	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)	t	0
2.0ms	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)	a	0

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`prod-diff_binary64`
247×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
216×	`log-pow_binary64`
138×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	274	31
2	3391	31

Stop Event

1×	node limit

Counts

2 → 59

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

896×	`fma-neg_binary64`
366×	`associate-/l*_binary64`
298×	`fma-def_binary64`
225×	`distribute-rgt-neg-in_binary64`
221×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	1692
1	72	1524
2	189	1524
3	504	1524
4	1230	1524
5	2449	1524
6	3577	1524
7	4684	1524

Stop Event

1×	node limit

Counts

167 → 73

prune78.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Error

0.1b

Counts

75 → 10

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)
	7.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2)) (cbrt.f64 a)))
	7.1b	(pow.f64 (/.f64 a (fma.f64 x (.f64 y 1/2) (.f64 (*.f64 t z) -9/2))) -1)
	34.4b	(*.f64 x (/.f64 1/2 (/.f64 a y)))
	30.9b	(.f64 t (.f64 z (/.f64 -9/2 a)))
▶	7.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))
	7.1b	(.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2)) (/.f64 1 a))
	7.9b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (.f64 y 1/2) (.f64 (*.f64 t z) -9/2)) a)) 3)
	7.9b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (.f64 y 1/2) (.f64 (*.f64 t z) -9/2))) 3) a)
	23.5b	(/.f64 (.f64 (cbrt.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2))) (cbrt.f64 (pow.f64 (fma.f64 x (.f64 y 1/2) (.f64 (*.f64 t z) -9/2)) 2))) a)

Compiler

Compiled 1630 to 1002 computations (38.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))
✓	0.2b	(.f64 9/2 (/.f64 (.f64 t z) a))
✓	5.8b	(/.f64 (*.f64 t z) a)
✓	6.6b	(/.f64 (*.f64 y x) a)

series83.0ms (1.1%)

Counts

4 → 24

Calls

42 calls:

4.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))	t	inf
4.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))	y	-inf
3.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))	y	inf
3.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))	x	-inf
3.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))	x	0

rewrite81.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

305×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
162×	`egg-rr`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	339	43
2	4779	43

Stop Event

1×	node limit

Counts

4 → 162

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary64`
364×	`associate-/l*_binary64`
270×	`fma-def_binary64`
224×	`distribute-rgt-neg-in_binary64`
215×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	348
1	59	324
2	163	324
3	450	324
4	1123	324
5	2377	324
6	3602	324
7	4706	324

Stop Event

1×	node limit

Counts

186 → 169

prune180.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	170	9	179

Error

Counts

179 → 9

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)
	7.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2)) (cbrt.f64 a)))
	22.2b	(-.f64 (.f64 1/2 (cbrt.f64 (pow.f64 (.f64 (/.f64 y a) x) 3))) (.f64 9/2 (/.f64 (.f64 t z) a)))
▶	5.5b	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))
	30.9b	(.f64 t (.f64 z (/.f64 -9/2 a)))
	7.7b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (.f64 t (*.f64 z (/.f64 1 a)))))
	7.7b	(fma.f64 (*.f64 (/.f64 y a) x) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a z) t)))
	7.9b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (.f64 z (*.f64 t (/.f64 1 a)))))
	7.9b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (.f64 y 1/2) (.f64 (*.f64 t z) -9/2))) 3) a)

Compiler

Compiled 4124 to 1919 computations (53.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))
	0.2b	(.f64 9/2 (/.f64 (.f64 t z) a))
✓	4.7b	(*.f64 (/.f64 y 1) (/.f64 x a))
	5.8b	(/.f64 (*.f64 t z) a)

series56.0ms (0.8%)

Counts

2 → 96

Calls

24 calls:

6.0ms	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))	z	0
3.0ms	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))	y	inf
3.0ms	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))	y	-inf
3.0ms	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))	x	0
3.0ms	(-.f64 (.f64 1/2 (.f64 (/.f64 y 1) (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))	a	inf

rewrite75.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`log1p-udef_binary64`
178×	`add-sqr-sqrt_binary64`
167×	`add-cbrt-cube_binary64`
167×	`log1p-expm1-u_binary64`
167×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	385	27
2	4991	27

Stop Event

1×	node limit

Counts

2 → 96

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
366×	`associate-/l*_binary64`
295×	`fma-def_binary64`
224×	`distribute-rgt-neg-in_binary64`
220×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	1284
1	69	1188
2	183	1188
3	490	1188
4	1212	1188
5	2434	1188
6	3492	1188
7	4606	1188

Stop Event

1×	node limit

Counts

192 → 105

prune159.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	173	8	181

Error

Counts

181 → 8

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)
	7.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2)) (cbrt.f64 a)))
▶	5.7b	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))
	30.9b	(.f64 t (.f64 z (/.f64 -9/2 a)))
	7.3b	(-.f64 (.f64 1/2 (/.f64 x (.f64 (/.f64 1 y) a))) (.f64 9/2 (/.f64 (.f64 t z) a)))
	7.7b	(fma.f64 (*.f64 (/.f64 y a) x) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a z) t)))
	7.9b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (.f64 z (*.f64 t (/.f64 1 a)))))
	5.7b	(-.f64 (.f64 1/2 (/.f64 y (/.f64 a x))) (.f64 9/2 (/.f64 (*.f64 t z) a)))

Compiler

Compiled 4236 to 2073 computations (51.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))
✓	0.2b	(/.f64 -9/2 (/.f64 (/.f64 a t) z))
✓	4.7b	(/.f64 (/.f64 a t) z)
✓	4.7b	(*.f64 y (/.f64 x a))

series92.0ms (1.2%)

Counts

4 → 168

Calls

42 calls:

5.0ms	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))	a	-inf
5.0ms	(/.f64 (/.f64 a t) z)	a	inf
4.0ms	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))	x	0
4.0ms	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))	t	0
3.0ms	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))	z	0

rewrite85.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

282×	`log1p-udef_binary64`
224×	`prod-diff_binary64`
157×	`add-sqr-sqrt_binary64`
146×	`add-log-exp_binary64`
146×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	308	44
2	4236	44

Stop Event

1×	node limit

Counts

4 → 116

simplify106.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-neg_binary64`
364×	`associate-/l*_binary64`
302×	`fma-def_binary64`
224×	`distribute-rgt-neg-in_binary64`
210×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	1896
1	72	1800
2	185	1800
3	496	1800
4	1231	1800
5	2452	1800
6	3577	1800
7	4679	1800

Stop Event

1×	node limit

Counts

284 → 127

prune106.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	128	7	135

Error

Counts

135 → 7

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (fma.f64 t (.f64 z -9/2) (.f64 x (/.f64 y 2))) a)
	7.8b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 (fma.f64 x (.f64 y 1/2) (.f64 (.f64 t z) -9/2)) (cbrt.f64 a)))
✓	5.7b	(fma.f64 (*.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a t) z)))
	5.5b	(fma.f64 (.f64 y (/.f64 x a)) 1/2 (/.f64 -9/2 (/.f64 a (.f64 t z))))
	7.3b	(-.f64 (.f64 1/2 (/.f64 x (.f64 (/.f64 1 y) a))) (.f64 9/2 (/.f64 (.f64 t z) a)))
	7.7b	(fma.f64 (*.f64 (/.f64 y a) x) 1/2 (/.f64 -9/2 (/.f64 (/.f64 a z) t)))
	5.7b	(-.f64 (.f64 1/2 (/.f64 y (/.f64 a x))) (.f64 9/2 (/.f64 (*.f64 t z) a)))

Compiler

Compiled 2456 to 1050 computations (57.2% saved)

regimes2.1s (29.1%)

Accuracy

Total 0.6b remaining (95.2%)

Threshold costs 0.6b (95.2%)

Counts

86 → 5

Compiler

Compiled 19359 to 13932 computations (28% saved)

bsearch3.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

Steps

Iters	Point		Range
3.874140262510758e+182	∈ [	3.874140262510758e+182	,	2.248228979260658e+205	]
4.265431290348826e-182	∈ [	4.265431290348826e-182	,	1.607158871217896e-179	]
-5.9208085336124974e-117	∈ [	-5.9208085336124974e-117	,	-2.607191047982696e-120	]
-2.540492647148833e+263	∈ [	-2.540492647148833e+263	,	-1.1680268255252614e+261	]

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`distribute-rgt-neg-in_binary64`
7×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	171
1	72	171
2	96	171
3	114	171
4	129	171
5	134	171
6	135	171

Stop Event

1×

saturated

end449.0ms (6.1%)

Stop Event

1×

fuel

Compiler

Compiled 873 to 525 computations (39.9% saved)

Details

analyze1.6s (21.2%)

sample1.7s (22.4%)

preprocess46.0ms (0.6%)

simplify38.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0.2%)

series51.0ms (0.7%)

rewrite56.0ms (0.8%)

simplify89.0ms (1.2%)

prune78.0ms (1.1%)

localize14.0ms (0.2%)

series83.0ms (1.1%)

rewrite81.0ms (1.1%)

simplify49.0ms (0.7%)

prune180.0ms (2.4%)

localize12.0ms (0.2%)

series56.0ms (0.8%)

rewrite75.0ms (1%)

simplify75.0ms (1%)

prune159.0ms (2.2%)

localize10.0ms (0.1%)

series92.0ms (1.2%)

rewrite85.0ms (1.1%)

simplify106.0ms (1.4%)

prune106.0ms (1.4%)

regimes2.1s (29.1%)

bsearch3.0ms (0%)

simplify10.0ms (0.1%)

end449.0ms (6.1%)

Profiling