Details

analyze2.7s (19.7%)

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
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample5.0s (35.8%)

Results

2.5s	2760×	body	1024	valid
851.0ms	3608×	body	128	valid
798.0ms	1279×	body	512	valid
322.0ms	1425×	body	128	invalid
258.0ms	599×	body	256	valid
95.0ms	153×	body	512	invalid
61.0ms	63×	body	1024	invalid
41.0ms	95×	body	256	invalid
21.0ms	10×	body	2048	valid

Compiler

Compiled 58 to 44 computations (24.1% saved)

preprocess36.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

924×	`times-frac_binary64`
389×	`associate-l_binary64`
386×	`associate-*l/_binary64`
361×	`associate-r_binary64`
301×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	152
1	171	140
2	687	140
3	4497	140
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 21 computations (25% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-/r/_binary64`
398×	`associate-/r*_binary64`
395×	`fma-def_binary64`
380×	`distribute-rgt-out_binary64`
325×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	55	35
2	193	35
3	1146	35
4	4817	35

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	33.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
▶	29.9b	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))

Status

Error

Program

33.2b

(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))

▶

29.9b

(*.f64 l (*.f64 (/.f64 (/.f64 2 (*.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))

Compiler

Compiled 159 to 114 computations (28.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.4b	(*.f64 (pow.f64 t 3) (sin.f64 k))
✓	4.9b	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
✓	7.9b	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)
✓	17.8b	(/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

series539.0ms (3.9%)

Counts

4 → 100

Calls

30 calls:

73.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	-inf
66.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))	l	-inf
62.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	inf
49.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	0
47.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))	l	inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`
187×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	105
1	408	105

Stop Event

1×	node limit

Counts

4 → 93

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

521×	`times-frac_binary64`
379×	`associate-/l*_binary64`
372×	`associate-/r*_binary64`
286×	`associate-r_binary64`
236×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	334	6037
1	1253	5945

Stop Event

1×	node limit

Counts

193 → 183

prune336.0ms (2.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	167	16	183
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	168	17	185

Error

9.6b

Counts

185 → 17

Alt Table

Status	Error	Program
▶	24.6b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	27.5b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	40.4b	(.f64 l (/.f64 (/.f64 (.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2)) (pow.f64 t 3)))
	27.8b	(.f64 l (/.f64 (.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	44.7b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (sqrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) (sqrt.f64 (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
	28.0b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
	34.2b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	32.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))
	24.6b	(.f64 l (.f64 2 (/.f64 l (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 (sin.f64 k) 2)) (cos.f64 k))) (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))))
	33.2b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	33.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	28.0b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	34.8b	(.f64 l (fma.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 (/.f64 (cos.f64 k) (pow.f64 k 4)) (/.f64 (.f64 t l) (pow.f64 (sin.f64 k) 2))) -4)))
	32.1b	(.f64 l (.f64 2 (/.f64 (.f64 (cos.f64 k) l) (.f64 (pow.f64 k 2) (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	54.8b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 (sqrt.f64 (sin.f64 k)) (pow.f64 t 3/2)) 2)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	25.6b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	34.4b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))

Compiler

Compiled 7818 to 4806 computations (38.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(.f64 (/.f64 (.f64 k k) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))
✓	5.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	8.0b	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))
✓	8.3b	(*.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))

series342.0ms (2.5%)

Counts

4 → 88

Calls

27 calls:

77.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	0
62.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	-inf
62.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	inf
10.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	t	-inf
9.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	k	inf

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`
174×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	89
1	386	89

Stop Event

1×	node limit

Counts

4 → 103

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

338×	`associate-/r/_binary64`
307×	`cancel-sign-sub-inv_binary64`
198×	`times-frac_binary64`
165×	`associate-r_binary64`
165×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	3179
1	616	3134
2	2728	2987

Stop Event

1×	node limit

Counts

191 → 159

prune374.0ms (2.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	150	9	159
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	155	21	176

Error

9.1b

Counts

176 → 21

Alt Table

Status	Error	Program
	49.8b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	33.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	24.6b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	34.8b	(.f64 l (fma.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 (/.f64 (cos.f64 k) (pow.f64 k 4)) (/.f64 (.f64 t l) (pow.f64 (sin.f64 k) 2))) -4)))
	44.7b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (sqrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) (sqrt.f64 (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
	28.0b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
▶	17.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	39.7b	(.f64 l (.f64 2 (.f64 1/2 (.f64 (/.f64 l (pow.f64 t 3)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))))
	52.4b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (.f64 (*.f64 (sin.f64 k) (sqrt.f64 t)) (/.f64 k (sqrt.f64 (cos.f64 k)))) 2)))))
	24.6b	(.f64 l (.f64 2 (pow.f64 (/.f64 (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 t (.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (.f64 k k) (cos.f64 k))))) l) -1)))
	34.2b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	32.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))
	31.9b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.4b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	27.5b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	21.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))
	33.2b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	24.8b	(.f64 l (.f64 2 (.f64 l (/.f64 1 (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 t (.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (*.f64 k k) (cos.f64 k)))))))))
	27.8b	(.f64 l (/.f64 (.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	28.0b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	25.6b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))

Compiler

Compiled 7598 to 4442 computations (41.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	5.5b	(.f64 (/.f64 (.f64 k k) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))
	5.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	8.0b	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))

series769.0ms (5.5%)

Counts

2 → 66

Calls

18 calls:

105.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	-inf
102.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	inf
100.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	0
98.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	0
97.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	inf

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`
217×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	100
1	491	92

Stop Event

1×	node limit

Counts

2 → 41

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-/r/_binary64`
363×	`fma-def_binary64`
350×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`
242×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	3966
1	638	3918
2	2993	3726

Stop Event

1×	node limit

Counts

107 → 89

prune378.0ms (2.7%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	2	18	20
Picked	0	1	1
Done	0	0	0
Total	150	22	172

Error

8.9b

Counts

172 → 22

Alt Table

Status	Error	Program
	24.8b	(.f64 l (.f64 2 (.f64 l (/.f64 1 (fma.f64 2 (.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (pow.f64 t 3) (cos.f64 k))) (.f64 (.f64 (/.f64 k (/.f64 (cos.f64 k) k)) t) (pow.f64 (sin.f64 k) 2)))))))
▶	21.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))
	49.8b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	33.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	44.7b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (sqrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) (sqrt.f64 (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
	28.0b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
✓	17.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	39.7b	(.f64 l (.f64 2 (.f64 1/2 (.f64 (/.f64 l (pow.f64 t 3)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2))))))
	52.4b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (.f64 (*.f64 (sin.f64 k) (sqrt.f64 t)) (/.f64 k (sqrt.f64 (cos.f64 k)))) 2)))))
	24.6b	(.f64 l (.f64 2 (pow.f64 (/.f64 (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 t (.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (.f64 k k) (cos.f64 k))))) l) -1)))
	34.2b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	32.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))
	30.8b	(.f64 (.f64 2 (/.f64 (cos.f64 k) (.f64 k k))) (.f64 (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2)) l))
	31.9b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.4b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	27.5b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	33.2b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	28.6b	(.f64 2 (/.f64 (pow.f64 l 2) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 (sin.f64 k) 2)) (cos.f64 k))) (/.f64 (.f64 (pow.f64 k 2) (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))))
	27.8b	(.f64 l (/.f64 (.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	28.0b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	24.6b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	25.6b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))

Compiler

Compiled 7466 to 4223 computations (43.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))
	5.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	8.0b	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))
	8.3b	(*.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))

series498.0ms (3.6%)

Counts

2 → 72

Calls

18 calls:

65.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))	l	0
63.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))	l	-inf
62.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))	l	inf
62.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))	l	-inf
60.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))	l	inf

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

216×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
200×	`add-cbrt-cube_binary64`
200×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	438	92

Stop Event

1×	node limit

Counts

2 → 41

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
434×	`times-frac_binary64`
316×	`associate-/l*_binary64`
283×	`associate-/r*_binary64`
230×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4572
1	902	4522
2	4232	4520

Stop Event

1×	node limit

Counts

113 → 101

prune399.0ms (2.9%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	151	9	160
Fresh	7	13	20
Picked	1	0	1
Done	0	1	1
Total	159	23	182

Error

8.3b

Counts

182 → 23

Alt Table

Status	Error	Program
	27.5b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	21.3b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (pow.f64 (cbrt.f64 (*.f64 t (pow.f64 (sin.f64 k) 2))) 3)) (/.f64 (cos.f64 k) k))))))
	21.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (pow.f64 t 3)) (cos.f64 k)) (/.f64 (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (/.f64 (cos.f64 k) k))))))
	24.8b	(.f64 l (.f64 2 (.f64 l (/.f64 1 (fma.f64 2 (.f64 (pow.f64 (sin.f64 k) 2) (/.f64 (pow.f64 t 3) (cos.f64 k))) (.f64 (.f64 (/.f64 k (/.f64 (cos.f64 k) k)) t) (pow.f64 (sin.f64 k) 2)))))))
	42.7b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k (pow.f64 (*.f64 (sin.f64 k) (sqrt.f64 t)) 2)) (/.f64 (cos.f64 k) k))))))
	33.2b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	21.2b	(pow.f64 (cbrt.f64 (.f64 l (/.f64 (.f64 2 l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 k (/.f64 (/.f64 (cos.f64 k) k) (.f64 t (pow.f64 (sin.f64 k) 2)))))))) 3)
	21.3b	(.f64 l (.f64 2 (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) 1) (/.f64 (cbrt.f64 l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 k (/.f64 (/.f64 (cos.f64 k) k) (*.f64 t (pow.f64 (sin.f64 k) 2)))))))))
	28.6b	(.f64 2 (/.f64 (pow.f64 l 2) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 (sin.f64 k) 2)) (cos.f64 k))) (/.f64 (.f64 (pow.f64 k 2) (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))))
	21.3b	(.f64 l (.f64 2 (.f64 l (/.f64 1 (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 k (/.f64 (/.f64 (cos.f64 k) k) (*.f64 t (pow.f64 (sin.f64 k) 2)))))))))
	27.8b	(.f64 l (/.f64 (.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	34.1b	(/.f64 (*.f64 (/.f64 l k) (/.f64 l k)) (pow.f64 t 3))
	28.0b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	44.7b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (sqrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (/.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) (sqrt.f64 (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
✓	17.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	34.2b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	32.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))
	30.8b	(.f64 (.f64 2 (/.f64 (cos.f64 k) (.f64 k k))) (.f64 (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2)) l))
	31.4b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) t))))
	49.8b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	24.6b	(.f64 2 (/.f64 l (/.f64 (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 (.f64 (*.f64 k k) (pow.f64 (sin.f64 k) 2)) t) (cos.f64 k))) l)))
	25.6b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	31.9b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))

Compiler

Compiled 7655 to 4587 computations (40.1% saved)

regimes1.2s (8.4%)

Accuracy

Total 3.9b remaining (31.4%)

Threshold costs 0b (0%)

Counts

117 → 4

Compiler

Compiled 20536 to 14415 computations (29.8% saved)

bsearch307.0ms (2.2%)

Algorithm

3×	binary-search

Calls

3 calls:

116.0ms	t
112.0ms	t
74.0ms	t

Steps

Iters	Point		Range
5.627754681832356e+102	∈ [	5.875811283662559e+96	,	4.7554555225048695e+103	]
1.3996591520002817e-64	∈ [	3.4437580008456118e-68	,	6.127948782968109e-61	]
-1.1025396404998137e-29	∈ [	-3.1644939040016427e-18	,	-1.9131018532851223e-31	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	187
1	79	187

Stop Event

1×

saturated

end473.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 978 to 651 computations (33.4% saved)

Details

analyze2.7s (19.7%)

sample5.0s (35.8%)

preprocess36.0ms (0.3%)

simplify23.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

series539.0ms (3.9%)

rewrite40.0ms (0.3%)

simplify76.0ms (0.5%)

prune336.0ms (2.4%)

localize19.0ms (0.1%)

series342.0ms (2.5%)

rewrite46.0ms (0.3%)

simplify62.0ms (0.4%)

prune374.0ms (2.7%)

localize22.0ms (0.2%)

series769.0ms (5.5%)

rewrite34.0ms (0.2%)

simplify75.0ms (0.5%)

prune378.0ms (2.7%)

localize19.0ms (0.1%)

series498.0ms (3.6%)

rewrite36.0ms (0.3%)

simplify91.0ms (0.7%)

prune399.0ms (2.9%)

regimes1.2s (8.4%)

bsearch307.0ms (2.2%)

simplify4.0ms (0%)

end473.0ms (3.4%)

Profiling