Details

analyze1.1s (7.4%)

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 (22%)

Alt Table

Status	Error	Program
▶	45.6b	(/.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))))

Results

902.0ms	5520×	body	128	valid
636.0ms	1181×	body	1024	valid
472.0ms	838×	body	1024	invalid
384.0ms	930×	body	512	valid
227.0ms	1507×	body	128	invalid
204.0ms	529×	body	512	invalid
151.0ms	541×	body	256	valid
79.0ms	290×	body	256	invalid
59.0ms	84×	body	2048	valid

Compiler

Compiled 152 to 102 computations (32.9% saved)

localize14.0ms (0.1%)

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))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	15.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
✓	22.5b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series1.8s (12.7%)

Counts

4 → 120

Calls

4 calls:

1.4s	(/.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))))
347.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
94.0ms	(-.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)

rewrite89.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

249×	`prod-diff_binary64`
213×	`add-sqr-sqrt_binary64`
206×	`log1p-expm1-u_binary64`
206×	`expm1-log1p-u_binary64`
202×	`add-log-exp_binary64`

Counts

4 → 131

Calls

4 calls:

83.0ms	(/.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))))
83.0ms	(*.f64 (sqrt.f64 2) t)
83.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
83.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	105
1	434	105
2	4732	105
3	5120	105
0	0	0
1	0	0

prune550.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	241	10	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	242	10	252

Error

7.5b

Counts

252 → 10

Alt Table

Status	Error	Program
	45.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (neg.f64 (.f64 (pow.f64 (cbrt.f64 l) 2) (cbrt.f64 (pow.f64 l 4))))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (pow.f64 l 4)) (*.f64 (pow.f64 (cbrt.f64 l) 2) (cbrt.f64 (pow.f64 l 4)))))))
	63.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)) l))
▶	36.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 2))) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) x)) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) x)) (.f64 2 (pow.f64 t 2))))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (.f64 2 (/.f64 x (-.f64 x 1))))) t))
	55.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 x 1))) (/.f64 (fma.f64 l l (.f64 2 (.f64 t t))) (sqrt.f64 (-.f64 x 1))) (neg.f64 (.f64 (.f64 l l) 1))) (fma.f64 (neg.f64 (.f64 l l)) 1 (.f64 (.f64 l l) 1)))))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	50.3b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 t 2) x) (-.f64 x 1))) (*.f64 2 (/.f64 (pow.f64 t 2) (-.f64 x 1)))))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))

Compiler

Compiled 27093 to 20963 computations (22.6% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.5b	(/.f64 (pow.f64 l 2) (pow.f64 x 2))
✓	20.0b	(/.f64 (pow.f64 t 2) (pow.f64 x 2))
✓	21.2b	(/.f64 (pow.f64 t 2) (pow.f64 x 3))
✓	30.7b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 2))) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) x)) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) x)) (*.f64 2 (pow.f64 t 2)))))))))

series640.0ms (4.4%)

Counts

4 → 32

Calls

4 calls:

545.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 2))) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) x)) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) x)) (*.f64 2 (pow.f64 t 2)))))))))
35.0ms	(/.f64 (pow.f64 t 2) (pow.f64 x 3))
30.0ms	(/.f64 (pow.f64 l 2) (pow.f64 x 2))
29.0ms	(/.f64 (pow.f64 t 2) (pow.f64 x 2))

rewrite70.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

347×	`log1p-expm1-u_binary64`
347×	`expm1-log1p-u_binary64`
330×	`add-log-exp_binary64`
329×	`add-exp-log_binary64`
319×	`pow1_binary64`

Counts

4 → 72

Calls

4 calls:

67.0ms	(/.f64 (pow.f64 l 2) (pow.f64 x 2))
67.0ms	(/.f64 (pow.f64 t 2) (pow.f64 x 2))
67.0ms	(/.f64 (pow.f64 t 2) (pow.f64 x 3))
67.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 2))) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) x)) (+.f64 (.f64 4 (/.f64 (pow.f64 t 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) x)) (*.f64 2 (pow.f64 t 2)))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	110
1	737	110
2	4876	110
3	4941	110
0	0	0
1	0	0

prune283.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	104	10	114

Error

0.7b

Counts

114 → 10

Alt Table

Status	Error	Program
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))))))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (.f64 2 (/.f64 x (-.f64 x 1))))) t))
	42.9b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.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)))))))) 3/2)))
▶	36.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (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)))))))))) 2))
	44.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.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)))))))) 3/2) 1/3))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))

Compiler

Compiled 14978 to 11359 computations (24.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	20.0b	(/.f64 (.f64 t t) (.f64 x x))
✓	21.2b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	30.7b	(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)))))))))

series641.0ms (4.4%)

Counts

4 → 104

Calls

4 calls:

546.0ms	(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)))))))))
35.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
31.0ms	(/.f64 (.f64 t t) (.f64 x x))
28.0ms	(/.f64 (.f64 l l) (.f64 x x))

rewrite73.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
255×	`add-log-exp_binary64`
254×	`add-cbrt-cube_binary64`
254×	`add-exp-log_binary64`

Counts

4 → 79

Calls

4 calls:

69.0ms	(/.f64 (.f64 l l) (.f64 x x))
69.0ms	(/.f64 (.f64 t t) (.f64 x x))
69.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
69.0ms	(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)))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	562	96
2	4778	96
3	5022	96
0	0	0
1	0	0

prune366.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	181	12	193

Error

0.7b

Counts

193 → 12

Alt Table

Status	Error	Program
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))))) 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))))))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (.f64 2 (/.f64 x (-.f64 x 1))))) t))
▶	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (.f64 l l) x))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (.f64 l l) x)))))))))))) 2))
✓	36.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (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)))))))))) 2))
	44.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.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)))))))) 3/2) 1/3))
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x)))))) 2))

Compiler

Compiled 19908 to 13025 computations (34.6% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.4b	(/.f64 (*.f64 l l) (pow.f64 x 3))
✓	21.2b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	30.7b	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))
✓	31.6b	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))

series1.6s (10.9%)

Counts

4 → 116

Calls

4 calls:

993.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))
524.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))
34.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
33.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))

rewrite77.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

258×	`log1p-expm1-u_binary64`
258×	`expm1-log1p-u_binary64`
254×	`add-cbrt-cube_binary64`
254×	`add-log-exp_binary64`
253×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

72.0ms	(/.f64 (*.f64 l l) (pow.f64 x 3))
72.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
72.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))
72.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (*.f64 l l) x)))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	164
1	575	164
2	4771	164
3	4865	164
0	0	0
1	0	0

prune1.2s (8.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	274	12	286

Error

0.7b

Counts

286 → 12

Alt Table

Status	Error	Program
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))))) 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))))))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 -1 (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (.f64 2 (/.f64 1 (-.f64 x 1))) (.f64 2 (/.f64 x (-.f64 x 1))))) t))
✓	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (.f64 l l) x))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (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 (.f64 l l) x)))))))))))) 2))
✓	36.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (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)))))))))) 2))
	44.0b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.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)))))))) 3/2) 1/3))
	39.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x)))))) 2))

Compiler

Compiled 53430 to 36081 computations (32.5% saved)

regimes1.3s (9.2%)

Accuracy

Total 10.6b remaining (95.7%)

Threshold costs 0b (0%)

Counts

59 → 8

Compiler

Compiled 20476 to 14091 computations (31.2% saved)

bsearch1.0s (7%)

Steps

Iters	Range		Point
9	4.927547754811477e-50	5.222058546902677e-43	5.140420865775031e-43
4	8.323539737805838e-203	1.250201860997097e-202	8.418248280997763e-203
7	9.561890316620867e-277	2.8180299637923408e-275	2.7904332859958544e-275
9	-1.2277242586577986e-222	-3.0724542176165685e-232	-1.2062010810487966e-222
10	-1.432676743906907e-186	-1.6680561949275367e-196	-1.4178637038882688e-186
7	-3.0249216193976242e-152	-1.901639390264525e-154	-1.9442302404542524e-154
10	-1.8970513977058847e+25	-14188174178012.344	-5.617995743088974e+23

Compiler

Compiled 4 to 3 computations (25% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
11×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	412
1	127	412
2	135	412
3	140	412
4	145	412
5	147	412
6	145	412

end399.0ms (2.7%)

Compiler: Compiled 1055 to 771 computations (26.9% saved)

Details

analyze1.1s (7.4%)

sample3.2s (22%)

localize14.0ms (0.1%)

series1.8s (12.7%)

rewrite89.0ms (0.6%)

prune550.0ms (3.8%)

localize32.0ms (0.2%)

series640.0ms (4.4%)

rewrite70.0ms (0.5%)

prune283.0ms (1.9%)

localize28.0ms (0.2%)

series641.0ms (4.4%)

rewrite73.0ms (0.5%)

prune366.0ms (2.5%)

localize36.0ms (0.2%)

series1.6s (10.9%)

rewrite77.0ms (0.5%)

prune1.2s (8.1%)

regimes1.3s (9.2%)

bsearch1.0s (7%)

simplify12.0ms (0.1%)

end399.0ms (2.7%)

Profiling