Details

analyze1.1s (11.5%)

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)

sample3.1s (32.8%)

Results

859.0ms	5495×	body	128	valid
613.0ms	1172×	body	1024	valid
441.0ms	860×	body	1024	invalid
373.0ms	943×	body	512	valid
247.0ms	1623×	body	128	invalid
217.0ms	569×	body	512	invalid
200.0ms	571×	body	256	valid
69.0ms	269×	body	256	invalid
50.0ms	75×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify23.0ms (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

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

43.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.6b	(/.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))))

Compiler

Compiled 116 to 75 computations (35.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.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))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	14.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
✓	20.0b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series998.0ms (10.4%)

Counts

4 → 120

Calls

4 calls:

728.0ms	(/.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))))
192.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
74.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
206×	`log1p-expm1-u_binary64`
206×	`expm1-log1p-u_binary64`
204×	`add-cbrt-cube_binary64`
200×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	105
1	437	105

Stop Event

1×	node limit

Counts

4 → 122

Calls

4 calls:

60.0ms	(/.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))))
60.0ms	(*.f64 (sqrt.f64 2) t)
60.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
59.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify191.0ms (2%)

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

242 → 279

prune842.0ms (8.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	271	8	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	8	280

Error

6.7b

Counts

280 → 8

Alt Table

Status	Error	Program
	58.9b	(*.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))))
	58.6b	(/.f64 (.f64 (sqrt.f64 2) t) (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)))))))
	58.4b	(/.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))))))))
▶	34.1b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	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))))))))
	38.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	58.8b	(neg.f64 (*.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)))))
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))

Compiler

Compiled 42549 to 31572 computations (25.8% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	15.7b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.7b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	17.8b	(/.f64 (.f64 t t) (.f64 x x))
✓	28.0b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

series417.0ms (4.4%)

Counts

4 → 104

Calls

4 calls:

335.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))
28.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
27.0ms	(/.f64 (.f64 l l) (.f64 x x))
26.0ms	(/.f64 (.f64 t t) (.f64 x x))

rewrite44.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
256×	`add-cbrt-cube_binary64`
253×	`add-cube-cbrt_binary64`
253×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	563	96

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

42.0ms	(/.f64 (.f64 l l) (.f64 x x))
42.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
42.0ms	(/.f64 (.f64 t t) (.f64 x x))
42.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
291×	`associate-l_binary64`
246×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	11996
1	1728	9975

Stop Event

1×	node limit

Counts

183 → 138

prune396.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Error

0.2b

Counts

146 → 9

Alt Table

Status	Error	Program
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))))
▶	34.7b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)))))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (/.f64 l (/.f64 t l)) (.f64 x x)) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 2 (/.f64 4 x)) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (fma.f64 t (sqrt.f64 (+.f64 (+.f64 2 (/.f64 4 x)) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 2 (/.f64 4 x)) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (+.f64 (.f64 (/.f64 l t) (/.f64 l (pow.f64 x 3))) (.f64 (/.f64 l t) (/.f64 l x))))))))
✓	34.1b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (pow.f64 x 3))) (.f64 2 (.f64 (/.f64 t x) (/.f64 t x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 t t) (.f64 2 (/.f64 t (/.f64 x t))))) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))
	41.0b	(/.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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))

Compiler

Compiled 21012 to 14113 computations (32.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) t)
✓	0.5b	(*.f64 x (sqrt.f64 2))
✓	2.5b	(/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l))
✓	5.8b	(/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)

series77.0ms (0.8%)

Counts

3 → 84

Calls

3 calls:

50.0ms	(/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l))
22.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)
4.0ms	(*.f64 x (sqrt.f64 2))

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
187×	`log-pow_binary64`
135×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	234	33
2	3185	33

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

56.0ms	(*.f64 x (sqrt.f64 2))
56.0ms	(/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l))
56.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

645×	`times-frac_binary64`
456×	`*-commutative_binary64`
409×	`associate-/l*_binary64`
330×	`unswap-sqr_binary64`
301×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	1044
1	24	1044
2	61	1044
3	178	1044
4	665	1044
5	3392	1044
6	3556	1044
7	4152	1044
8	4263	1044
9	4409	1044
10	4582	1044

Stop Event

1×	node limit

Counts

197 → 118

prune148.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	136	8	144

Error

0.2b

Counts

144 → 8

Alt Table

Status	Error	Program
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))))
✓	34.1b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (pow.f64 x 3))) (.f64 2 (.f64 (/.f64 t x) (/.f64 t x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 t t) (.f64 2 (/.f64 t (/.f64 x t))))) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
▶	11.8b	(/.f64 (fabs.f64 (.f64 t (sqrt.f64 2))) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)))))
	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))
	41.0b	(/.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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))

Compiler

Compiled 5256 to 3515 computations (33.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 t (sqrt.f64 2))
	0.5b	(*.f64 x (sqrt.f64 2))
	2.5b	(/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l))
	5.8b	(/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)

series3.0ms (0%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 t (sqrt.f64 2))

rewrite31.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
335×	`pow1_binary64`
247×	`unpow-prod-down_binary64`
204×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1080	6

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

31.0ms

(*.f64 t (sqrt.f64 2))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

33 → 33

prune161.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	151	8	159

Error

0.2b

Counts

159 → 8

Alt Table

Status	Error	Program
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))))
✓	34.1b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (pow.f64 x 3))) (.f64 2 (.f64 (/.f64 t x) (/.f64 t x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l))))))) (+.f64 (.f64 t t) (.f64 2 (/.f64 t (/.f64 x t))))) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
✓	11.8b	(/.f64 (fabs.f64 (.f64 t (sqrt.f64 2))) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (sqrt.f64 2) (.f64 x t)) l)))))
	35.0b	(/.f64 (.f64 (sqrt.f64 2) t) (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))
	41.0b	(/.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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))

Compiler

Compiled 5530 to 3776 computations (31.7% saved)

regimes1.2s (12%)

Accuracy

Total 12.0b remaining (95.4%)

Threshold costs 0b (0%)

Counts

112 → 3

Compiler

Compiled 32158 to 22113 computations (31.2% saved)

bsearch162.0ms (1.7%)

Steps

Iters	Range		Point
6	1.6840210283824452e+245	1.7374425123595308e+246	3.3598491021846746e+245
9	4.357781641374015e+163	8.988520407456828e+168	8.858220110000705e+168

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	133
1	46	133
2	47	133

Stop Event

1×

saturated

end267.0ms (2.8%)

Compiler: Compiled 665 to 438 computations (34.1% saved)

Details

analyze1.1s (11.5%)

sample3.1s (32.8%)

simplify23.0ms (0.2%)

prune3.0ms (0%)

localize17.0ms (0.2%)

series998.0ms (10.4%)

rewrite63.0ms (0.7%)

simplify191.0ms (2%)

prune842.0ms (8.8%)

localize29.0ms (0.3%)

series417.0ms (4.4%)

rewrite44.0ms (0.5%)

simplify117.0ms (1.2%)

prune396.0ms (4.1%)

localize14.0ms (0.1%)

series77.0ms (0.8%)

rewrite58.0ms (0.6%)

simplify90.0ms (0.9%)

prune148.0ms (1.5%)

localize16.0ms (0.2%)

series3.0ms (0%)

rewrite31.0ms (0.3%)

simplify6.0ms (0.1%)

prune161.0ms (1.7%)

regimes1.2s (12%)

bsearch162.0ms (1.7%)

simplify3.0ms (0%)

end267.0ms (2.8%)

Profiling