Details

analyze1.5s (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Compiler

Compiled 26 to 20 computations (23.1% saved)

sample4.2s (32.4%)

Results

1.2s	1658×	body	1024	valid
932.0ms	4769×	body	128	valid
825.0ms	730×	body	2048	valid
673.0ms	3491×	body	128	invalid
385.0ms	751×	body	512	valid
150.0ms	345×	body	256	valid
9.0ms	3×	body	4096	valid

Compiler

Compiled 52 to 40 computations (23.1% saved)

preprocess57.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

424×	`fma-neg_binary64`
394×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`
334×	`sub-neg_binary64`
202×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	464
1	280	464
2	569	464
3	1059	432
4	2182	400
5	4013	400
0	6	6
1	6	6

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort z t)

Compiler

Compiled 25 to 19 computations (24% saved)

simplify42.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-def_binary64`
437×	`fma-neg_binary64`
148×	`cancel-sign-sub-inv_binary64`
110×	`distribute-rgt-neg-in_binary64`
108×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	34	29
2	65	29
3	120	27
4	241	25
5	399	25
6	639	25
7	922	25
8	1213	25
9	1748	25
10	2412	25
11	2780	25
12	2871	25
13	2887	25
14	2887	25

Stop Event

1×

saturated

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

20.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.6b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
▶	20.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (/.f64 -1/3 b)))

Compiler

Compiled 138 to 101 computations (26.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))
✓	0.3b	(*.f64 t -1/3)
✓	0.4b	(/.f64 -1/3 b)
✓	24.8b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series36.0ms (0.3%)

Counts

4 → 84

Calls

27 calls:

3.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))	x	0
3.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))	x	-inf
3.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))	z	0
3.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))	x	inf
3.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))	t	0

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`log-prod_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
218×	`log-pow_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	263	33
2	3134	33

Stop Event

1×	node limit

Counts

4 → 86

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

729×	`associate-l_binary64`
653×	`associate-r_binary64`
364×	`cancel-sign-sub-inv_binary64`
320×	`fma-def_binary64`
220×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1491
1	280	1422
2	990	1366
3	4819	1366

Stop Event

1×	node limit

Counts

170 → 124

prune235.0ms (1.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	100	24	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	101	25	126

Error

14.5b

Counts

126 → 25

Alt Table

Status	Error	Program
	39.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	24.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 2))) (*.f64 a (/.f64 -1/3 b)))
	34.4b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	37.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (sqrt.f64 (/.f64 1/9 (.f64 b b)))))
	20.6b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.8b	(fma.f64 2 (cbrt.f64 (.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 3) (pow.f64 x 3/2))) (*.f64 a (/.f64 -1/3 b)))
	20.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (pow.f64 (.f64 b -3) -1)))
	44.6b	(fma.f64 2 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (.f64 a (/.f64 -1/3 b)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (pow.f64 (cbrt.f64 (/.f64 -1/3 b)) 3)))
	20.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (.f64 -1/3 (/.f64 1 b))))
	19.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (-.f64 (.f64 (cos.f64 (.f64 z (.f64 t -1/3))) (cos.f64 y)) (.f64 (sin.f64 (.f64 z (.f64 t -1/3))) (sin.f64 y)))) (.f64 a (/.f64 -1/3 b)))
▶	16.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))
	20.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x))) 3) (*.f64 a (/.f64 -1/3 b)))
	35.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (-.f64 (exp.f64 (log1p.f64 (/.f64 -1/3 b))) 1)))
	38.6b	(fma.f64 2 (pow.f64 (pow.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)) 3) 1/3) (*.f64 a (/.f64 -1/3 b)))
	20.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	53.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (sqrt.f64 (.f64 t -1/3)) 2) y))) (*.f64 a (/.f64 -1/3 b)))
	20.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (*.f64 a (/.f64 -1/3 b)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (cbrt.f64 (.f64 t -1/3)) 3) y))) (*.f64 a (/.f64 -1/3 b)))
	40.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (+.f64 (.f64 (sin.f64 (.f64 t (.f64 z -1/3))) (-.f64 (.f64 1/6 (pow.f64 y 3)) y)) (.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (.f64 (.f64 y y) -1/2))))) (*.f64 a (/.f64 -1/3 b)))
	28.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	24.4b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 2))) (*.f64 a (/.f64 -1/3 b)))
	20.8b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	40.1b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (sin.f64 1)))) (.f64 a (/.f64 -1/3 b)))
	35.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t)))) y))) (.f64 a (/.f64 -1/3 b)))

Compiler

Compiled 4548 to 3002 computations (34% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))
✓	0.2b	(*.f64 (sqrt.f64 x) (cos.f64 y))
✓	0.3b	(*.f64 a (/.f64 -1/3 b))
	0.4b	(/.f64 -1/3 b)

series45.0ms (0.3%)

Counts

3 → 73

Calls

24 calls:

3.0ms	(*.f64 (sqrt.f64 x) (cos.f64 y))	y	0
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))	y	-inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))	x	-inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))	y	inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))	x	inf

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

604×	`log-prod_binary64`
240×	`prod-diff_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
211×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	267	33
2	3151	33

Stop Event

1×	node limit

Counts

3 → 74

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

644×	`cancel-sign-sub-inv_binary64`
503×	`fma-neg_binary64`
426×	`sub-neg_binary64`
200×	`*-commutative_binary64`
173×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	1026
1	137	960
2	406	934
3	1435	925
4	4226	925

Stop Event

1×	node limit

Counts

147 → 97

prune228.0ms (1.7%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	114	33	147

Error

14.3b

Counts

147 → 33

Alt Table

Status	Error	Program
	28.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	33.7b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))) 2)
	17.2b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 3) (.f64 a (/.f64 -1/3 b)))
	34.4b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	37.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (sqrt.f64 (/.f64 1/9 (.f64 b b)))))
	49.6b	(pow.f64 (pow.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b)) 3) 1/3)
	20.6b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.8b	(fma.f64 2 (cbrt.f64 (.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 3) (pow.f64 x 3/2))) (*.f64 a (/.f64 -1/3 b)))
	28.4b	(/.f64 (-.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (pow.f64 (/.f64 (.f64 a -1/3) b) 2)) (-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (*.f64 a -1/3) b)))
	28.3b	(fma.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) 1) (.f64 a (/.f64 -1/3 b)))
	37.1b	(fma.f64 (sqrt.f64 x) (-.f64 2 (*.f64 y y)) (/.f64 -1/3 (/.f64 b a)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (pow.f64 (cbrt.f64 (/.f64 -1/3 b)) 3)))
	40.5b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) 3) (pow.f64 (/.f64 (.f64 a -1/3) b) 3)) (fma.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (-.f64 (pow.f64 (/.f64 (.f64 a -1/3) b) 2) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (.f64 a -1/3) b)))))
	24.4b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 2))) (*.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (expm1.f64 (log1p.f64 (/.f64 (.f64 a -1/3) b))))
	25.4b	(-.f64 (.f64 2 (sqrt.f64 x)) (.f64 1/3 (/.f64 a b)))
	19.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (-.f64 (.f64 (cos.f64 (.f64 z (.f64 t -1/3))) (cos.f64 y)) (.f64 (sin.f64 (.f64 z (.f64 t -1/3))) (sin.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	17.6b	(.f64 (cbrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))) (pow.f64 (cbrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (*.f64 a -1/3) b))) 2))
	20.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x))) 3) (*.f64 a (/.f64 -1/3 b)))
	35.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (-.f64 (exp.f64 (log1p.f64 (/.f64 -1/3 b))) 1)))
	21.3b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	38.6b	(fma.f64 2 (pow.f64 (pow.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)) 3) 1/3) (*.f64 a (/.f64 -1/3 b)))
	20.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	53.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (sqrt.f64 (.f64 t -1/3)) 2) y))) (*.f64 a (/.f64 -1/3 b)))
	20.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (*.f64 a (/.f64 -1/3 b)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (cbrt.f64 (.f64 t -1/3)) 3) y))) (*.f64 a (/.f64 -1/3 b)))
	40.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (+.f64 (.f64 (sin.f64 (.f64 t (.f64 z -1/3))) (-.f64 (.f64 1/6 (pow.f64 y 3)) y)) (.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (.f64 (.f64 y y) -1/2))))) (*.f64 a (/.f64 -1/3 b)))
	35.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t)))) y))) (.f64 a (/.f64 -1/3 b)))
	21.1b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2))) (.f64 a (/.f64 -1/3 b)))
	39.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	20.8b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	40.1b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (sin.f64 1)))) (.f64 a (/.f64 -1/3 b)))
▶	16.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))

Compiler

Compiled 3980 to 2583 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))
	0.2b	(*.f64 (sqrt.f64 x) (cos.f64 y))
✓	0.2b	(/.f64 (*.f64 a -1/3) b)
✓	0.4b	(*.f64 a -1/3)

series37.0ms (0.3%)

Counts

3 → 73

Calls

21 calls:

3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))	y	0
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))	y	-inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))	x	inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))	x	-inf
3.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))	y	inf

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

306×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
212×	`log-pow_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	266	29
2	3251	29

Stop Event

1×	node limit

Counts

3 → 82

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
377×	`associate-l_binary64`
371×	`cancel-sign-sub-inv_binary64`
300×	`fma-neg_binary64`
293×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	920
1	100	857
2	270	845
3	886	838
4	3924	838

Stop Event

1×	node limit

Counts

155 → 96

prune217.0ms (1.7%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	31	32
Picked	0	1	1
Done	0	0	0
Total	123	33	156

Error

14.3b

Counts

156 → 33

Alt Table

Status	Error	Program
	28.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	33.7b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))) 2)
▶	17.2b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 3) (.f64 a (/.f64 -1/3 b)))
	34.4b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	37.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (sqrt.f64 (/.f64 1/9 (.f64 b b)))))
	49.6b	(pow.f64 (pow.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b)) 3) 1/3)
	20.6b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.8b	(fma.f64 2 (cbrt.f64 (.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 3) (pow.f64 x 3/2))) (*.f64 a (/.f64 -1/3 b)))
	28.4b	(/.f64 (-.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (pow.f64 (/.f64 (.f64 a -1/3) b) 2)) (-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (*.f64 a -1/3) b)))
	28.3b	(fma.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) 1) (.f64 a (/.f64 -1/3 b)))
	37.1b	(fma.f64 (sqrt.f64 x) (-.f64 2 (*.f64 y y)) (/.f64 -1/3 (/.f64 b a)))
	25.4b	(fma.f64 -1/3 (/.f64 a b) (*.f64 2 (sqrt.f64 x)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (pow.f64 (cbrt.f64 (/.f64 -1/3 b)) 3)))
	40.5b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) 3) (pow.f64 (/.f64 (.f64 a -1/3) b) 3)) (fma.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (-.f64 (pow.f64 (/.f64 (.f64 a -1/3) b) 2) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (.f64 a -1/3) b)))))
	24.4b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 2))) (*.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (expm1.f64 (log1p.f64 (/.f64 (.f64 a -1/3) b))))
	19.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (-.f64 (.f64 (cos.f64 (.f64 z (.f64 t -1/3))) (cos.f64 y)) (.f64 (sin.f64 (.f64 z (.f64 t -1/3))) (sin.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	17.6b	(.f64 (cbrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))) (pow.f64 (cbrt.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (*.f64 a -1/3) b))) 2))
	20.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x))) 3) (*.f64 a (/.f64 -1/3 b)))
	35.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (-.f64 (exp.f64 (log1p.f64 (/.f64 -1/3 b))) 1)))
	21.3b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	38.6b	(fma.f64 2 (pow.f64 (pow.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)) 3) 1/3) (*.f64 a (/.f64 -1/3 b)))
	20.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	53.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (sqrt.f64 (.f64 t -1/3)) 2) y))) (*.f64 a (/.f64 -1/3 b)))
	20.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (*.f64 a (/.f64 -1/3 b)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (cbrt.f64 (.f64 t -1/3)) 3) y))) (*.f64 a (/.f64 -1/3 b)))
	40.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (+.f64 (.f64 (sin.f64 (.f64 t (.f64 z -1/3))) (-.f64 (.f64 1/6 (pow.f64 y 3)) y)) (.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (.f64 (.f64 y y) -1/2))))) (*.f64 a (/.f64 -1/3 b)))
	35.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t)))) y))) (.f64 a (/.f64 -1/3 b)))
	21.1b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2))) (.f64 a (/.f64 -1/3 b)))
	39.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	20.8b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	40.1b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (sin.f64 1)))) (.f64 a (/.f64 -1/3 b)))
✓	16.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))

Compiler

Compiled 3954 to 2496 computations (36.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 a (/.f64 -1/3 b))
	0.4b	(/.f64 -1/3 b)
✓	0.6b	(cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y))) 3)

series432.0ms (3.3%)

Counts

2 → 40

Calls

12 calls:

74.0ms	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y))) 3)	y	-inf
73.0ms	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y))) 3)	y	inf
70.0ms	(cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y)))	y	-inf
67.0ms	(cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y)))	y	inf
36.0ms	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (cos.f64 y))) 3)	x	0

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
356×	`log-prod_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	179	18
2	1889	18

Stop Event

1×	node limit

Counts

2 → 65

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
385×	`*-commutative_binary64`
367×	`distribute-rgt-neg-in_binary64`
365×	`distribute-lft-neg-in_binary64`
222×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	494
1	127	483
2	435	458
3	1972	450

Stop Event

1×	node limit

Counts

105 → 81

prune206.0ms (1.6%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	9	22	31
Picked	1	0	1
Done	0	1	1
Total	135	33	168

Error

14.3b

Counts

168 → 33

Alt Table

Status	Error	Program
	39.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	30.2b	(fma.f64 2 (pow.f64 (exp.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))))) 3) (.f64 a (/.f64 -1/3 b)))
	28.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	21.3b	(fma.f64 2 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2)))) 3) (.f64 a (/.f64 -1/3 b)))
	34.4b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	37.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (sqrt.f64 (/.f64 1/9 (.f64 b b)))))
	17.6b	(fma.f64 2 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) 3) 3) (.f64 a (/.f64 -1/3 b)))
	20.6b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.8b	(fma.f64 2 (cbrt.f64 (.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 3) (pow.f64 x 3/2))) (*.f64 a (/.f64 -1/3 b)))
	30.4b	(fma.f64 2 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 1/3) (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 1/3)) 3) (.f64 a (/.f64 -1/3 b)))
	28.3b	(fma.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) 1) (.f64 a (/.f64 -1/3 b)))
	37.1b	(fma.f64 (sqrt.f64 x) (-.f64 2 (*.f64 y y)) (/.f64 -1/3 (/.f64 b a)))
	25.4b	(fma.f64 -1/3 (/.f64 a b) (*.f64 2 (sqrt.f64 x)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (pow.f64 (cbrt.f64 (/.f64 -1/3 b)) 3)))
	24.4b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 2))) (*.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (expm1.f64 (log1p.f64 (/.f64 (.f64 a -1/3) b))))
	20.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x))) 3) (*.f64 a (/.f64 -1/3 b)))
	35.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (*.f64 a (-.f64 (exp.f64 (log1p.f64 (/.f64 -1/3 b))) 1)))
	38.6b	(fma.f64 2 (pow.f64 (pow.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)) 3) 1/3) (*.f64 a (/.f64 -1/3 b)))
	17.0b	(fma.f64 2 (.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (cos.f64 y))) (*.f64 a (/.f64 -1/3 b)))
	17.1b	(fma.f64 2 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 x)) (cos.f64 y))) (*.f64 a (/.f64 -1/3 b)))
✓	16.9b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))
	53.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (sqrt.f64 (.f64 t -1/3)) 2) y))) (*.f64 a (/.f64 -1/3 b)))
	17.0b	(fma.f64 2 (.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) (sqrt.f64 x))) (*.f64 a (/.f64 -1/3 b)))
	20.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (cbrt.f64 (.f64 t -1/3)) 3) y))) (*.f64 a (/.f64 -1/3 b)))
	40.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (+.f64 (.f64 (sin.f64 (.f64 t (.f64 z -1/3))) (-.f64 (.f64 1/6 (pow.f64 y 3)) y)) (.f64 (cos.f64 (.f64 1/3 (.f64 t z))) (.f64 (.f64 y y) -1/2))))) (*.f64 a (/.f64 -1/3 b)))
	26.0b	(fma.f64 2 (pow.f64 (pow.f64 x 1/6) 3) (*.f64 a (/.f64 -1/3 b)))
	35.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) t)))) y))) (.f64 a (/.f64 -1/3 b)))
	30.3b	(fma.f64 2 (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 1/3)) 3) (*.f64 a (/.f64 -1/3 b)))
	18.4b	(fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 x 1/6)) 3) (.f64 a (/.f64 -1/3 b)))
	19.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (-.f64 (.f64 (cos.f64 (.f64 z (.f64 t -1/3))) (cos.f64 y)) (.f64 (sin.f64 (.f64 z (.f64 t -1/3))) (sin.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	20.8b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))) (.f64 a (/.f64 -1/3 b)))
	40.1b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (fma.f64 z (.f64 t -1/3) y)))) (sin.f64 1)))) (.f64 a (/.f64 -1/3 b)))

Compiler

Compiled 3534 to 2150 computations (39.2% saved)

regimes4.6s (35.1%)

Accuracy

Total 1.6b remaining (10%)

Threshold costs 0b (0%)

Counts

165 → 3

Compiler

Compiled 71600 to 55516 computations (22.5% saved)

bsearch7.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(*.f64 z t)
0.0ms	(*.f64 z t)

Steps

Iters	Point		Range
5.757236538346392e+129	∈ [	5.757236538346392e+129	,	1.6902929196708876e+153	]
-1.785357164967349e+147	∈ [	-1.785357164967349e+147	,	-2.3905065691948453e+140	]

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	91
1	58	91
2	75	91
3	86	91
4	93	91
5	96	91
6	97	91

Stop Event

1×

saturated

end713.0ms (5.4%)

Stop Event

1×

fuel

Compiler

Compiled 1133 to 843 computations (25.6% saved)

Details

analyze1.5s (11.7%)

sample4.2s (32.4%)

preprocess57.0ms (0.4%)

simplify42.0ms (0.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series36.0ms (0.3%)

rewrite65.0ms (0.5%)

simplify59.0ms (0.5%)

prune235.0ms (1.8%)

localize9.0ms (0.1%)

series45.0ms (0.3%)

rewrite54.0ms (0.4%)

simplify57.0ms (0.4%)

prune228.0ms (1.7%)

localize11.0ms (0.1%)

series37.0ms (0.3%)

rewrite55.0ms (0.4%)

simplify46.0ms (0.4%)

prune217.0ms (1.7%)

localize12.0ms (0.1%)

series432.0ms (3.3%)

rewrite48.0ms (0.4%)

simplify33.0ms (0.3%)

prune206.0ms (1.6%)

regimes4.6s (35.1%)

bsearch7.0ms (0.1%)

simplify7.0ms (0.1%)

end713.0ms (5.4%)

Profiling