Details

analyze1.1s (8.9%)

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
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample3.2s (26.4%)

Results

909.0ms	5438×	body	128	valid
637.0ms	1198×	body	1024	valid
451.0ms	863×	body	1024	invalid
415.0ms	958×	body	512	valid
252.0ms	1579×	body	128	invalid
197.0ms	487×	body	512	invalid
162.0ms	574×	body	256	valid
75.0ms	290×	body	256	invalid
64.0ms	88×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
506×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
259×	`distribute-rgt-neg-in_binary64`
215×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	117	39
3	267	39
4	618	39
5	1427	39
6	3153	39

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

40.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
▶	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))

Status

Error

Program

40.2b

(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))

▶

40.2b

(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l)))))

Compiler

Compiled 174 to 115 computations (33.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	14.7b	(fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))
✓	18.6b	(sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))))

series877.0ms (7.2%)

Counts

4 → 120

Calls

4 calls:

664.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
168.0ms	(sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))))
42.0ms	(fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

199×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
185×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	105
1	420	99

Stop Event

1×	node limit

Counts

4 → 104

Calls

4 calls:

50.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
50.0ms	(*.f64 (sqrt.f64 2) t)
50.0ms	(fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))
50.0ms	(sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))))

simplify175.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

632×	`*-commutative_binary64`
385×	`fma-def_binary64`
342×	`associate-+r+_binary64`
278×	`associate-r_binary64`
225×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688

Stop Event

1×	node limit

Counts

224 → 261

prune828.0ms (6.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	250	11	261
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	251	12	263

Error

4.0b

Counts

263 → 12

Alt Table

Status	Error	Program
✓	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	50.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 t (sqrt.f64 2))) 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	58.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))) (/.f64 t (/.f64 l (sqrt.f64 2))))
	35.3b	(.f64 t (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (/.f64 (*.f64 t t) (+.f64 x -1))))))))
	58.0b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1))) l (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))) (+.f64 (.f64 (/.f64 (.f64 t t) l) (/.f64 x (+.f64 x -1))) (/.f64 (.f64 t t) (.f64 l (+.f64 x -1))))))))
	58.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	40.4b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1))))))))
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
▶	29.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	40.6b	(/.f64 (pow.f64 (cbrt.f64 (.f64 t (sqrt.f64 2))) 3) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))

Compiler

Compiled 41494 to 30926 computations (25.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.6b	(/.f64 (*.f64 t t) x)
✓	13.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.7b	(/.f64 (.f64 t t) (.f64 x x))
✓	25.5b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

series199.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

142.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))
24.0ms	(/.f64 (.f64 t t) (.f64 x x))
24.0ms	(/.f64 (.f64 l l) (.f64 x x))
9.0ms	(/.f64 (*.f64 t t) x)

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

206×	`add-sqr-sqrt_binary64`
198×	`log1p-expm1-u_binary64`
198×	`expm1-log1p-u_binary64`
197×	`add-cbrt-cube_binary64`
196×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	81
1	426	67

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

39.0ms	(/.f64 (*.f64 t t) x)
39.0ms	(/.f64 (.f64 l l) (.f64 x x))
39.0ms	(/.f64 (.f64 t t) (.f64 x x))
39.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
289×	`associate-/r*_binary64`
277×	`associate-r_binary64`
249×	`associate-l_binary64`
221×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	7585
1	1348	6486

Stop Event

1×	node limit

Counts

229 → 188

prune314.0ms (2.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	179	9	188
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	185	15	200

Error

0.2b

Counts

200 → 15

Alt Table

Status	Error	Program
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 3/2)))
	33.1b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	50.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 t (sqrt.f64 2))) 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	36.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t x)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))))))
	35.3b	(.f64 t (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (/.f64 (*.f64 t t) (+.f64 x -1))))))))
	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	26.5b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3))
▶	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2))
	40.6b	(/.f64 (pow.f64 (cbrt.f64 (.f64 t (sqrt.f64 2))) 3) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))

Compiler

Compiled 15765 to 9633 computations (38.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) t)
✓	1.0b	(fma.f64 t t (/.f64 l (/.f64 x l)))
✓	4.2b	(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))
✓	25.5b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2)

series316.0ms (2.6%)

Counts

3 → 108

Calls

3 calls:

247.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2)

54.0ms

(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))

14.0ms

(fma.f64 t t (/.f64 l (/.f64 x l)))

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

210×	`add-sqr-sqrt_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
198×	`add-log-exp_binary64`
197×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	91
1	452	89

Stop Event

1×	node limit

Counts

3 → 56

Calls

3 calls:

34.0ms

(fma.f64 t t (/.f64 l (/.f64 x l)))

34.0ms

(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))

34.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2)

simplify104.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

588×	`times-frac_binary64`
566×	`associate-/r*_binary64`
491×	`fma-def_binary64`
472×	`associate-/l*_binary64`
190×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	491	10984
1	1788	10217

Stop Event

1×	node limit

Counts

164 → 143

prune334.0ms (2.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	3	10	13
Picked	0	1	1
Done	0	1	1
Total	158	15	173

Error

0.2b

Counts

173 → 15

Alt Table

Status	Error	Program
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t x)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))))))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 3/2)))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	50.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 t (sqrt.f64 2))) 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	40.8b	(/.f64 (cbrt.f64 (pow.f64 (.f64 t (sqrt.f64 2)) 3)) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2))
	40.6b	(/.f64 (pow.f64 (cbrt.f64 (.f64 t (sqrt.f64 2))) 3) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	36.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
	35.3b	(.f64 t (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (/.f64 (*.f64 t t) (+.f64 x -1))))))))
▶	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	38.5b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (/.f64 (/.f64 l (/.f64 t l)) t) (+.f64 (/.f64 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 (log.f64 t) 2))) (.f64 (.f64 x x) (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (/.f64 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 (log.f64 t) 2))) (.f64 x (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))) (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (*.f64 (log.f64 t) 2)))))
✓	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2))

Compiler

Compiled 18098 to 12569 computations (30.6% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)
	1.0b	(fma.f64 t t (/.f64 l (/.f64 x l)))
	4.2b	(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))
✓	26.2b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4)

series637.0ms (5.2%)

Counts

2 → 72

Calls

2 calls:

389.0ms

(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)

247.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4)

rewrite34.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

217×	`add-sqr-sqrt_binary64`
213×	`log1p-expm1-u_binary64`
213×	`expm1-log1p-u_binary64`
207×	`add-cbrt-cube_binary64`
207×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	94
1	477	93

Stop Event

1×	node limit

Counts

2 → 35

Calls

2 calls:

32.0ms

(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)

32.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4)

simplify182.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

361×	`*-commutative_binary64`
251×	`+-commutative_binary64`
197×	`fma-def_binary64`
184×	`associate-+r+_binary64`
135×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	939	19666
1	3638	18321

Stop Event

1×	node limit

Counts

107 → 163

prune636.0ms (5.2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	227	15	242

Error

0.2b

Counts

242 → 15

Alt Table

Status	Error	Program
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t x)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (+.f64 (.f64 (/.f64 (pow.f64 l 2) (.f64 t (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))))))))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 3/2)))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	50.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 t (sqrt.f64 2))) 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	40.8b	(/.f64 (cbrt.f64 (pow.f64 (.f64 t (sqrt.f64 2)) 3)) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2))
	40.6b	(/.f64 (pow.f64 (cbrt.f64 (.f64 t (sqrt.f64 2))) 3) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
	36.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
	35.3b	(.f64 t (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (/.f64 (*.f64 t t) (+.f64 x -1))))))))
✓	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	38.5b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (/.f64 (/.f64 l (/.f64 t l)) t) (+.f64 (/.f64 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 (log.f64 t) 2))) (.f64 (.f64 x x) (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (/.f64 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 (log.f64 t) 2))) (.f64 x (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))) (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (*.f64 (log.f64 t) 2)))))
✓	26.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/2))

Compiler

Compiled 32376 to 23393 computations (27.7% saved)

regimes2.0s (16.1%)

Accuracy

Total 8.6b remaining (92.3%)

Threshold costs 0b (0%)

Counts

123 → 5

Compiler

Compiled 27780 to 20267 computations (27% saved)

bsearch529.0ms (4.3%)

Steps

Iters	Range		Point
7	2.1619762343420863e+61	1.762798061039258e+63	1.7217277470457817e+63
9	-5.858506782973357e-274	-1.7561552091000522e-280	-5.760693106007019e-274
6	-1.2305667899749975e-205	-2.2145558220808283e-206	-2.238472624987465e-206
10	-0.008866260243616425	-2.77151334505108e-20	-0.008644579131846854

Compiler

Compiled 4 to 3 computations (25% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`*-commutative_binary64`
21×	`+-commutative_binary64`
15×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	280
1	105	280
2	133	280
3	154	280
4	178	280
5	196	280
6	206	280
7	211	280
8	212	280

Stop Event

1×

saturated

end432.0ms (3.5%)

Compiler: Compiled 1006 to 701 computations (30.3% saved)

Iter	Nodes	Cost
0	76	280
1	105	280
2	133	280
3	154	280
4	178	280
5	196	280
6	206	280
7	211	280
8	212	280

Iter	Nodes	Cost
0	76	280
1	105	280
2	133	280
3	154	280
4	178	280
5	196	280
6	206	280
7	211	280
8	212	280

Details

analyze1.1s (8.9%)

sample3.2s (26.4%)

simplify27.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series877.0ms (7.2%)

rewrite53.0ms (0.4%)

simplify175.0ms (1.4%)

prune828.0ms (6.8%)

localize20.0ms (0.2%)

series199.0ms (1.6%)

rewrite42.0ms (0.3%)

simplify77.0ms (0.6%)

prune314.0ms (2.6%)

localize28.0ms (0.2%)

series316.0ms (2.6%)

rewrite36.0ms (0.3%)

simplify104.0ms (0.9%)

prune334.0ms (2.7%)

localize28.0ms (0.2%)

series637.0ms (5.2%)

rewrite34.0ms (0.3%)

simplify182.0ms (1.5%)

prune636.0ms (5.2%)

regimes2.0s (16.1%)

bsearch529.0ms (4.3%)

simplify13.0ms (0.1%)

end432.0ms (3.5%)

Profiling

Iter	Nodes	Cost
0	76	280
1	105	280
2	133	280
3	154	280
4	178	280
5	196	280
6	206	280
7	211	280
8	212	280