Details

analyze2.5s (20.7%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
16.4%	83.5%	0.1%	9
24.6%	75.3%	0.1%	10
28.7%	71.2%	0.1%	11
30.7%	69.1%	0.1%	12
35.8%	64%	0.1%	13
38.4%	61.5%	0.1%	14

Compiler

Compiled 32 to 18 computations (43.8% saved)

sample5.3s (44.3%)

Results

2.8s	2054×	body	1024	valid
1.3s	4615×	body	128	valid
899.0ms	1095×	body	512	valid
269.0ms	484×	body	256	valid
28.0ms	8×	body	2048	valid

Compiler

Compiled 64 to 36 computations (43.8% saved)

preprocess21.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

48×	`fma-def_binary64`
44×	`*-commutative_binary64`
24×	`associate-r_binary64`
24×	`associate-l_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	176
1	105	176
2	193	176
3	241	176
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`fma-def_binary64`
11×	`*-commutative_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	44
1	30	44
2	52	44
3	64	44

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (+.f64 (.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 120 to 56 computations (53.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 ew (sin.f64 t))
✓	0.1b	(.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))
✓	2.0b	(/.f64 (/.f64 eh ew) (tan.f64 t))
✓	37.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series130.0ms (1.1%)

Counts

4 → 132

Calls

33 calls:

10.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))	t	-inf
9.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))	eh	0
9.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))	t	inf
9.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))	eh	-inf
8.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))	eh	inf

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
211×	`log-pow_binary64`
133×	`*-un-lft-identity_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	254	48
2	3495	48

Stop Event

1×	node limit

Counts

4 → 95

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
391×	`distribute-lft-neg-in_binary64`
387×	`distribute-rgt-neg-in_binary64`
260×	`associate-l_binary64`
232×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	2125
1	200	2049
2	681	1997
3	2637	1995

Stop Event

1×	node limit

Counts

227 → 125

prune144.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	4	177

Error

0.1b

Counts

177 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (+.f64 (.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	21.9b	(fabs.f64 (+.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 2) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.5b	(fabs.f64 (+.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	22.1b	(fabs.f64 (+.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 ew 3) (pow.f64 (sin.f64 t) 3))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 6255 to 1648 computations (73.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))
✓	0.7b	(cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3))
	2.0b	(/.f64 (/.f64 eh ew) (tan.f64 t))
	37.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series54.0ms (0.5%)

Counts

2 → 72

Calls

18 calls:

5.0ms	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))	ew	-inf
5.0ms	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))	ew	inf
4.0ms	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))	eh	inf
4.0ms	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))	ew	0
4.0ms	(.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3)))	eh	0

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
150×	`pow1_binary64`
149×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	323	33
2	4003	33

Stop Event

1×	node limit

Counts

2 → 43

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

696×	`cancel-sign-sub-inv_binary64`
590×	`distribute-rgt-neg-in_binary64`
505×	`distribute-lft-neg-in_binary64`
499×	`fma-neg_binary64`
288×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	1372
1	96	1304
2	324	1264
3	1426	1264
4	3903	1264

Stop Event

1×	node limit

Counts

115 → 54

prune207.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	180	4	184

Error

0.1b

Counts

184 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (+.f64 (.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	21.9b	(fabs.f64 (+.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 2) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
▶	0.5b	(fabs.f64 (+.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	22.1b	(fabs.f64 (+.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 ew 3) (pow.f64 (sin.f64 t) 3))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 6731 to 2045 computations (69.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 ew (sin.f64 t))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3)
	2.0b	(/.f64 (/.f64 eh ew) (tan.f64 t))
✓	21.2b	(cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t)))))

series1.1s (9.1%)

Counts

2 → 24

Calls

18 calls:

192.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	t	-inf
181.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	t	inf
169.0ms	(cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t)))))	t	-inf
162.0ms	(cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t)))))	t	inf
74.0ms	(pow.f64 (cbrt.f64 (/.f64 (*.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	ew	-inf

rewrite63.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
146×	`pow1_binary64`
144×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	322	42
2	4083	42

Stop Event

1×	node limit

Counts

2 → 93

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

617×	`associate-r_binary64`
539×	`associate-l_binary64`
485×	`associate-/l*_binary64`
393×	`associate-/r*_binary64`
163×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1124
1	265	1088
2	1009	1082

Stop Event

1×	node limit

Counts

117 → 112

prune347.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	234	4	238
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	235	7	242

Error

0.0b

Counts

242 → 7

Alt Table

Status	Error	Program
	0.2b	(fabs.f64 (+.f64 (/.f64 ew (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (sin.f64 t))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	21.9b	(fabs.f64 (+.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 2) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.5b	(fabs.f64 (+.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.6b	(fabs.f64 (+.f64 (/.f64 (pow.f64 (cbrt.f64 ew) 2) (/.f64 (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (sin.f64 t)) (cbrt.f64 ew))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
▶	0.1b	(fabs.f64 (+.f64 (/.f64 1 (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t)))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.1b	(fabs.f64 (+.f64 (/.f64 (sin.f64 t) (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) ew)) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 9502 to 3465 computations (63.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t)))
✓	0.4b	(/.f64 1 (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t))))
	2.0b	(/.f64 (/.f64 eh ew) (tan.f64 t))
✓	3.3b	(/.f64 eh (*.f64 ew (tan.f64 t)))

series327.0ms (2.7%)

Counts

3 → 108

Calls

27 calls:

49.0ms	(/.f64 1 (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t))))	t	inf
48.0ms	(/.f64 1 (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t))))	t	-inf
22.0ms	(/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t)))	t	inf
22.0ms	(/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (.f64 ew (sin.f64 t)))	t	-inf
13.0ms	(/.f64 eh (*.f64 ew (tan.f64 t)))	t	-inf

rewrite64.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

247×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
140×	`add-sqr-sqrt_binary64`
138×	`pow1_binary64`
137×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	275	49
2	3791	49

Stop Event

1×	node limit

Counts

3 → 130

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
270×	`unswap-sqr_binary64`
265×	`times-frac_binary64`
229×	`associate-/l*_binary64`
211×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4461
1	829	4341
2	3699	4305

Stop Event

1×	node limit

Counts

238 → 206

prune387.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	259	5	264

Error

0.0b

Counts

264 → 5

Alt Table

Status	Error	Program
	0.2b	(fabs.f64 (+.f64 (/.f64 ew (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) (sin.f64 t))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 (.f64 ew (sin.f64 t)) (cbrt.f64 (pow.f64 (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) 3))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.5b	(fabs.f64 (+.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (sin.f64 t)) (hypot.f64 1 (/.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	1.4b	(fabs.f64 (+.f64 (/.f64 1 (/.f64 (/.f64 1 (sin.f64 t)) ew)) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.1b	(fabs.f64 (+.f64 (/.f64 (sin.f64 t) (/.f64 (hypot.f64 1 (/.f64 eh (.f64 ew (tan.f64 t)))) ew)) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 10846 to 4148 computations (61.8% saved)

regimes770.0ms (6.4%)

Accuracy

Total 0.0b remaining (34.6%)

Threshold costs 0.0b (34.6%)

Counts

118 → 1

Compiler

Compiled 19356 to 12354 computations (36.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	26	51

Stop Event

1×

saturated

end168.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 224 to 140 computations (37.5% saved)

Details

analyze2.5s (20.7%)

sample5.3s (44.3%)

preprocess21.0ms (0.2%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize21.0ms (0.2%)

series130.0ms (1.1%)

rewrite57.0ms (0.5%)

simplify56.0ms (0.5%)

prune144.0ms (1.2%)

localize23.0ms (0.2%)

series54.0ms (0.5%)

rewrite54.0ms (0.4%)

simplify50.0ms (0.4%)

prune207.0ms (1.7%)

localize22.0ms (0.2%)

series1.1s (9.1%)

rewrite63.0ms (0.5%)

simplify33.0ms (0.3%)

prune347.0ms (2.9%)

localize23.0ms (0.2%)

series327.0ms (2.7%)

rewrite64.0ms (0.5%)

simplify82.0ms (0.7%)

prune387.0ms (3.2%)

regimes770.0ms (6.4%)

simplify2.0ms (0%)

end168.0ms (1.4%)

Profiling