Details

analyze1.4s (13.3%)

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)

sample4.1s (38.3%)

Symmetry

(sort z t)

Results

1.1s	1580×	body	1024	valid
904.0ms	4818×	body	128	valid
851.0ms	753×	body	2048	valid
653.0ms	3522×	body	128	invalid
402.0ms	780×	body	512	valid
108.0ms	324×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify45.0ms (0.4%)

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

prune5.0ms (0.1%)

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

20.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.3b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
▶	21.2b	(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
✓	0.2b	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))
✓	0.3b	(/.f64 -1/3 b)
✓	0.3b	(*.f64 t -1/3)
✓	23.8b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series39.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))
10.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))
1.0ms	(*.f64 t -1/3)
1.0ms	(/.f64 -1/3 b)

rewrite60.0ms (0.6%)

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

Calls

4 calls:

59.0ms	(.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))
59.0ms	(/.f64 -1/3 b)
59.0ms	(*.f64 t -1/3)
59.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

simplify56.0ms (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

prune192.0ms (1.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	101	23	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	24	126

Error

13.6b

Counts

126 → 24

Alt Table

Status	Error	Program
	44.5b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (pow.f64 (.f64 t -1/3) 3) 1/3) y))) (*.f64 a (/.f64 -1/3 b)))
	21.7b	(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)))
	45.1b	(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)))
	38.9b	(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)))
	21.3b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.5b	(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)))
	21.2b	(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)))
	40.5b	(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)))
	21.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) 3))) (*.f64 a (/.f64 -1/3 b)))
	24.9b	(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)))
	29.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	39.5b	(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)))))
	21.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) 3)) (*.f64 a (/.f64 -1/3 b)))
	35.2b	(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)))
	21.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 a (.f64 (cbrt.f64 (/.f64 -1/3 b)) (pow.f64 (cbrt.f64 (/.f64 -1/3 b)) 2))))
	28.2b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	21.2b	(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))))
	26.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 1/3 (.f64 (sin.f64 y) (.f64 t z)) (cos.f64 y))) (.f64 a (/.f64 -1/3 b)))
	20.6b	(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)))
▶	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))
	24.9b	(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)))
	54.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (exp.f64 (log.f64 (.f64 t -1/3))) y))) (*.f64 a (/.f64 -1/3 b)))
	26.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (sqrt.f64 (.f64 (.f64 t t) 1/9)) y))) (.f64 a (/.f64 -1/3 b)))
	21.2b	(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)))

Compiler

Compiled 4420 to 2904 computations (34.3% 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 a (/.f64 -1/3 b)))
✓	0.2b	(*.f64 (sqrt.f64 x) (cos.f64 y))
✓	0.2b	(*.f64 a (/.f64 -1/3 b))
	0.3b	(/.f64 -1/3 b)

series46.0ms (0.4%)

Counts

3 → 73

Calls

3 calls:

31.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))
9.0ms	(*.f64 (sqrt.f64 x) (cos.f64 y))
6.0ms	(*.f64 a (/.f64 -1/3 b))

rewrite54.0ms (0.5%)

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

Calls

3 calls:

52.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (/.f64 -1/3 b)))
52.0ms	(*.f64 (sqrt.f64 x) (cos.f64 y))
52.0ms	(*.f64 a (/.f64 -1/3 b))

simplify49.0ms (0.5%)

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

prune214.0ms (2%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	104	18	122
Fresh	8	15	23
Picked	1	0	1
Done	0	0	0
Total	113	33	146

Error

13.4b

Counts

146 → 33

Alt Table

Status	Error	Program
	44.5b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (pow.f64 (.f64 t -1/3) 3) 1/3) y))) (*.f64 a (/.f64 -1/3 b)))
	21.7b	(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)))
	38.9b	(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)))
	16.2b	(fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))
	31.1b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	21.5b	(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)))
	21.2b	(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)))
	26.3b	(fma.f64 2 (cbrt.f64 (.f64 (pow.f64 x 3/2) (pow.f64 (cos.f64 y) 3))) (.f64 a (/.f64 -1/3 b)))
	16.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (*.f64 (/.f64 1 b) -1/3)))
	24.9b	(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)))
	29.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	37.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 1 (.f64 y (.f64 y -1/2)))) (.f64 a (/.f64 -1/3 b)))
	30.2b	(fma.f64 2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 2) (.f64 a (/.f64 -1/3 b)))
	21.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) 3)) (*.f64 a (/.f64 -1/3 b)))
	35.2b	(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)))
	41.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	16.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 3) (.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	26.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 1/3 (.f64 (sin.f64 y) (.f64 t z)) (cos.f64 y))) (.f64 a (/.f64 -1/3 b)))
	16.7b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (/.f64 (.f64 a -1/3) (pow.f64 (cbrt.f64 b) 2)) (cbrt.f64 b)))
	62.4b	(log.f64 (exp.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))))
	54.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (exp.f64 (log.f64 (.f64 t -1/3))) y))) (*.f64 a (/.f64 -1/3 b)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))
	16.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (pow.f64 (cbrt.f64 (/.f64 (.f64 a -1/3) b)) 3))
	20.6b	(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)))
▶	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 a (.f64 b -3)))
	50.8b	(pow.f64 (pow.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b)) 3) 1/3)
	26.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (sqrt.f64 (.f64 (.f64 t t) 1/9)) y))) (.f64 a (/.f64 -1/3 b)))
	16.9b	(.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))
	23.8b	(fma.f64 (sqrt.f64 x) 2 (/.f64 -1/3 (/.f64 b a)))
	26.3b	(fma.f64 2 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3)) (.f64 a (/.f64 -1/3 b)))
	19.7b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2))) (.f64 a (/.f64 -1/3 b)))
	21.2b	(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)))

Compiler

Compiled 3718 to 2411 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series46.0ms (0.4%)

Counts

3 → 65

Calls

3 calls:

38.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 a (.f64 b -3)))
6.0ms	(/.f64 a (*.f64 b -3))
1.0ms	(cos.f64 y)

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

288×	`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	28
1	266	28
2	3271	28

Stop Event

1×	node limit

Counts

3 → 85

Calls

3 calls:

50.0ms	(cos.f64 y)
50.0ms	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 a (.f64 b -3)))
50.0ms	(/.f64 a (*.f64 b -3))

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
536×	`associate-l_binary64`
489×	`cancel-sign-sub-inv_binary64`
421×	`associate-r_binary64`
411×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	928
1	133	861
2	365	845
3	1230	836

Stop Event

1×	node limit

Counts

150 → 104

prune221.0ms (2.1%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	8	24	32
Picked	1	0	1
Done	0	0	0
Total	133	31	164

Error

13.3b

Counts

164 → 31

Alt Table

Status	Error	Program
	44.5b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (pow.f64 (.f64 t -1/3) 3) 1/3) y))) (*.f64 a (/.f64 -1/3 b)))
	21.7b	(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)))
▶	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 y)))) (/.f64 a (.f64 b -3)))
	38.9b	(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)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (/.f64 a (.f64 b -3)))
	16.2b	(fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))
	31.1b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	21.5b	(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)))
	24.9b	(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)))
	29.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	19.7b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2))) (.f64 a (/.f64 -1/3 b)))
	33.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 y))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 y))) (sin.f64 1)))) (/.f64 a (.f64 b -3)))
	30.2b	(fma.f64 2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 2) (.f64 a (/.f64 -1/3 b)))
	35.2b	(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)))
	41.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	16.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 3) (.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	26.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 1/3 (.f64 (sin.f64 y) (.f64 t z)) (cos.f64 y))) (.f64 a (/.f64 -1/3 b)))
	16.7b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (/.f64 (.f64 a -1/3) (pow.f64 (cbrt.f64 b) 2)) (cbrt.f64 b)))
	62.4b	(log.f64 (exp.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))))
	54.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (exp.f64 (log.f64 (.f64 t -1/3))) y))) (*.f64 a (/.f64 -1/3 b)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))
	20.6b	(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)))
	50.8b	(pow.f64 (pow.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b)) 3) 1/3)
	26.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (sqrt.f64 (.f64 (.f64 t t) 1/9)) y))) (.f64 a (/.f64 -1/3 b)))
	23.7b	(fma.f64 2 (sqrt.f64 x) (/.f64 a (*.f64 b -3)))
	16.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (pow.f64 (.f64 -3 (/.f64 b a)) -1))
	16.9b	(.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))
	37.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 y (.f64 y -1/2) 1)) (/.f64 a (*.f64 b -3)))
	16.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (cos.f64 y)) 3)) (/.f64 a (.f64 b -3)))
	21.2b	(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)))

Compiler

Compiled 3802 to 2444 computations (35.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 y))))
	0.2b	(/.f64 a (*.f64 b -3))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series15.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(*.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 y))))
3.0ms	(expm1.f64 (cos.f64 y))
1.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite39.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`expm1-log1p-u_binary64`
566×	`log1p-expm1-u_binary64`
317×	`log-prod_binary64`
169×	`pow2_binary64`
119×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	139	16
2	1582	16

Stop Event

1×	node limit

Counts

3 → 69

Calls

3 calls:

38.0ms	(*.f64 (sqrt.f64 x) (log1p.f64 (expm1.f64 (cos.f64 y))))
38.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))
38.0ms	(expm1.f64 (cos.f64 y))

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
476×	`sub-neg_binary64`
243×	`*-commutative_binary64`
181×	`associate-+l-_binary64`
174×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	362
1	151	345
2	440	320
3	1689	312
4	4204	312

Stop Event

1×	node limit

Counts

105 → 93

prune248.0ms (2.3%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	0	30	30
Picked	1	0	1
Done	0	0	0
Total	129	35	164

Error

13.3b

Counts

164 → 35

Alt Table

Status	Error	Program
	44.5b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (pow.f64 (pow.f64 (.f64 t -1/3) 3) 1/3) y))) (*.f64 a (/.f64 -1/3 b)))
	21.7b	(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)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3)))) (/.f64 a (.f64 b -3)))
	38.9b	(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)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (/.f64 a (.f64 b -3)))
	16.2b	(fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))
	31.1b	(fma.f64 2 (exp.f64 (log.f64 (.f64 (sqrt.f64 x) (cos.f64 y)))) (.f64 a (/.f64 -1/3 b)))
	21.5b	(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)))
	19.7b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (sqrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 2)))) (/.f64 a (.f64 b -3)))
	24.9b	(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)))
	29.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 a (/.f64 -1/3 b)))
	19.7b	(fma.f64 2 (sqrt.f64 (.f64 x (pow.f64 (cos.f64 y) 2))) (.f64 a (/.f64 -1/3 b)))
	33.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 y))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 y))) (sin.f64 1)))) (/.f64 a (.f64 b -3)))
	16.5b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (.f64 (cbrt.f64 (expm1.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 y))) 2)))) (/.f64 a (*.f64 b -3)))
	30.2b	(fma.f64 2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 2) (.f64 a (/.f64 -1/3 b)))
	35.2b	(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)))
	16.4b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (cos.f64 y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (cos.f64 y)))))))) (/.f64 a (.f64 b -3)))
	41.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 a (exp.f64 (log.f64 (/.f64 -1/3 b)))))
	16.5b	(fma.f64 2 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (cos.f64 y))) 3) (.f64 a (/.f64 -1/3 b)))
	28.2b	(fma.f64 2 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)) (sqrt.f64 x)))) (*.f64 a (/.f64 -1/3 b)))
	26.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 1/3 (.f64 (sin.f64 y) (.f64 t z)) (cos.f64 y))) (.f64 a (/.f64 -1/3 b)))
	16.7b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (/.f64 (.f64 a -1/3) (pow.f64 (cbrt.f64 b) 2)) (cbrt.f64 b)))
	62.4b	(log.f64 (exp.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b))))
	54.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (exp.f64 (log.f64 (.f64 t -1/3))) y))) (*.f64 a (/.f64 -1/3 b)))
	16.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (/.f64 (.f64 a -1/3) b))
	20.6b	(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)))
	50.8b	(pow.f64 (pow.f64 (fma.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y) (/.f64 (.f64 a -1/3) b)) 3) 1/3)
	26.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (sqrt.f64 (.f64 (.f64 t t) 1/9)) y))) (.f64 a (/.f64 -1/3 b)))
	23.7b	(fma.f64 2 (sqrt.f64 x) (/.f64 a (*.f64 b -3)))
	16.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (pow.f64 (.f64 -3 (/.f64 b a)) -1))
	16.9b	(.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))
	21.2b	(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)))
	16.7b	(fma.f64 2 (.f64 (sqrt.f64 x) (log1p.f64 (fma.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 y))) 2) (cbrt.f64 (exp.f64 (cos.f64 y))) -1))) (/.f64 a (.f64 b -3)))
	37.6b	(fma.f64 2 (.f64 (sqrt.f64 x) (fma.f64 y (.f64 y -1/2) 1)) (/.f64 a (*.f64 b -3)))
	16.3b	(fma.f64 2 (.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (cos.f64 y)) 3)) (/.f64 a (.f64 b -3)))

Compiler

Compiled 3365 to 2023 computations (39.9% saved)

regimes2.9s (27.4%)

Accuracy

Total 1.7b remaining (10.3%)

Threshold costs 0b (0%)

Counts

115 → 3

Compiler

Compiled 50139 to 38473 computations (23.3% saved)

bsearch4.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	113
1	60	113
2	72	113
3	78	113
4	82	113
5	83	113

Stop Event

1×

saturated

end738.0ms (6.9%)

Compiler: Compiled 1197 to 890 computations (25.6% saved)

Details

analyze1.4s (13.3%)

sample4.1s (38.3%)

simplify45.0ms (0.4%)

prune5.0ms (0.1%)

localize13.0ms (0.1%)

series39.0ms (0.4%)

rewrite60.0ms (0.6%)

simplify56.0ms (0.5%)

prune192.0ms (1.8%)

localize11.0ms (0.1%)

series46.0ms (0.4%)

rewrite54.0ms (0.5%)

simplify49.0ms (0.5%)

prune214.0ms (2%)

localize11.0ms (0.1%)

series46.0ms (0.4%)

rewrite52.0ms (0.5%)

simplify32.0ms (0.3%)

prune221.0ms (2.1%)

localize15.0ms (0.1%)

series15.0ms (0.1%)

rewrite39.0ms (0.4%)

simplify35.0ms (0.3%)

prune248.0ms (2.3%)

regimes2.9s (27.4%)

bsearch4.0ms (0%)

simplify5.0ms (0.1%)

end738.0ms (6.9%)

Profiling