Details

analyze1.4s (13.5%)

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)

sample166.0ms (1.6%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

23.0ms	45×	body	1024	valid
17.0ms	23×	body	2048	valid
13.0ms	147×	body	128	valid
9.0ms	32×	body	512	valid
6.0ms	63×	body	128	nan
2.0ms	29×	body	128	invalid
2.0ms	9×	body	256	valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	34	29
2	64	29
3	114	27
4	209	25
5	322	25
6	494	25
7	644	25
8	810	25
9	979	25
10	1197	25
11	1297	25
12	1308	25
13	1324	25
14	1324	25
15	1213	25

prune5.0ms (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

20.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))

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 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
✓	0.3b	(*.f64 t -1/3)
✓	0.3b	(/.f64 -1/3 b)
✓	26.5b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series61.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

45.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
13.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))
2.0ms	(*.f64 t -1/3)
1.0ms	(/.f64 -1/3 b)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
3.0ms	(*.f64 t -1/3)
2.0ms	(/.f64 -1/3 b)
1.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

simplify139.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
414×	`fma-def_binary64`
405×	`distribute-rgt-neg-in_binary64`
387×	`cancel-sign-sub-inv_binary64`
371×	`distribute-lft-neg-in_binary64`

Counts

163 → 134

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	213	2679
1	521	2489
2	1581	2422
3	3043	2410
4	4687	2408
5	4981	2408
6	4938	2408

prune241.0ms (2.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	110	24	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	25	136

Error

14.5b

Counts

136 → 25

Alt Table

Status	Error	Program
	20.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3)) y))))
	20.6b	(fma.f64 a (.f64 (.f64 (cbrt.f64 (/.f64 -1/3 b)) (cbrt.f64 (/.f64 -1/3 b))) (cbrt.f64 (/.f64 -1/3 b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (*.f64 (pow.f64 t 3) -1/27)) y))))
	20.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)) 3))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))))
	54.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (exp.f64 (log.f64 (*.f64 t -1/3))) y))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (exp.f64 (log.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	35.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (expm1.f64 (log1p.f64 (*.f64 t -1/3))) y))))
	20.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.7b	(fma.f64 a (/.f64 (/.f64 -1/3 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (.f64 t -1/3)))))))
	20.3b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (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)))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.3b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	35.2b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)) (sqrt.f64 x))))))
	34.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (fma.f64 y (sin.f64 (.f64 1/3 (.f64 t z))) (cos.f64 (.f64 1/3 (.f64 t z))))))
	36.8b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) -1/3)) y))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 (.f64 t -1/3)) (cbrt.f64 (.f64 t -1/3))) (cbrt.f64 (*.f64 t -1/3))) y))))
▶	16.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

Compiler

Compiled 4944 to 3170 computations (35.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
✓	0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
	0.3b	(/.f64 -1/3 b)

series52.0ms (0.5%)

Counts

2 → 49

Calls

2 calls:

34.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
17.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

10.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-def_binary64`
549×	`cancel-sign-sub-inv_binary64`
370×	`sub-neg_binary64`
327×	`fma-neg_binary64`
256×	`*-commutative_binary64`

Counts

79 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1413
1	221	1267
2	710	1241
3	1413	1237
4	3235	1237
5	4500	1237
6	4919	1237

prune244.0ms (2.3%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	83	15	98
Fresh	7	17	24
Picked	1	0	1
Done	0	0	0
Total	91	32	123

Error

14.4b

Counts

123 → 32

Alt Table

Status	Error	Program
	17.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (fma.f64 y (sin.f64 (.f64 1/3 (.f64 t z))) (cos.f64 (.f64 1/3 (.f64 t z))))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) -1/3)) y))))
	37.1b	(.f64 (sqrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (sqrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	44.1b	(fma.f64 a (/.f64 -1/3 b) (log.f64 (exp.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	26.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	17.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3)))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))
	35.5b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 (.f64 t -1/3)) (cbrt.f64 (.f64 t -1/3))) (cbrt.f64 (*.f64 t -1/3))) y))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (*.f64 (pow.f64 t 3) -1/27)) y))))
	20.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)) 3))))
	33.7b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	16.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))))
	35.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (expm1.f64 (log1p.f64 (*.f64 t -1/3))) y))))
	25.3b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	16.8b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (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)))))
	17.3b	(fma.f64 a (/.f64 (/.f64 -1/3 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.1b	(*.f64 -1/3 (/.f64 a b))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.3b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
▶	16.8b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3)) y))))
	29.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (sqrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (exp.f64 (log.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (.f64 t -1/3)))))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))

Compiler

Compiled 3558 to 2271 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
✓	0.3b	(*.f64 -1/3 (/.f64 1 b))

series38.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

37.0ms	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
2.0ms	(*.f64 -1/3 (/.f64 1 b))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(*.f64 -1/3 (/.f64 1 b))
0.0ms	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify119.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`
315×	`fma-neg_binary64`
309×	`sub-neg_binary64`
260×	`*-commutative_binary64`

Counts

97 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1302
1	225	1157
2	481	1145
3	1296	1138
4	3667	1138
5	4642	1138
6	4993	1138
7	4936	1138

prune238.0ms (2.3%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	30	31
Picked	0	1	1
Done	0	0	0
Total	121	32	153

Error

14.4b

Counts

153 → 32

Alt Table

Status	Error	Program
	17.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (fma.f64 y (sin.f64 (.f64 1/3 (.f64 t z))) (cos.f64 (.f64 1/3 (.f64 t z))))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) -1/3)) y))))
	37.1b	(.f64 (sqrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (sqrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	44.1b	(fma.f64 a (/.f64 -1/3 b) (log.f64 (exp.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	26.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	17.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3)))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))
	35.5b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 (.f64 t -1/3)) (cbrt.f64 (.f64 t -1/3))) (cbrt.f64 (*.f64 t -1/3))) y))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (*.f64 (pow.f64 t 3) -1/27)) y))))
	20.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)) 3))))
	33.7b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	16.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))))
	35.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (expm1.f64 (log1p.f64 (*.f64 t -1/3))) y))))
	25.3b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
▶	16.8b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (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)))))
	17.2b	(fma.f64 a (.f64 (.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b)))) (cbrt.f64 (/.f64 1 b))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.1b	(*.f64 -1/3 (/.f64 a b))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.3b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
✓	16.8b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3)) y))))
	29.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (sqrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (exp.f64 (log.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (.f64 t -1/3)))))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))

Compiler

Compiled 4158 to 2702 computations (35% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
✓	0.4b	(/.f64 b -1/3)
✓	0.6b	(/.f64 1 (/.f64 b -1/3))

series42.0ms (0.4%)

Counts

3 → 61

Calls

3 calls:

38.0ms	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
2.0ms	(/.f64 1 (/.f64 b -1/3))
2.0ms	(/.f64 b -1/3)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 117

Calls

3 calls:

4.0ms	(/.f64 1 (/.f64 b -1/3))
2.0ms	(/.f64 b -1/3)
0.0ms	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
381×	`cancel-sign-sub-inv_binary64`
328×	`fma-neg_binary64`
241×	`times-frac_binary64`
223×	`unsub-neg_binary64`

Counts

178 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2421
1	277	2076
2	623	2035
3	1599	2028
4	4483	2028
5	4985	2028

prune361.0ms (3.4%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	2	28	30
Picked	0	1	1
Done	1	0	1
Total	220	31	251

Error

14.4b

Counts

251 → 31

Alt Table

Status	Error	Program
	17.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (fma.f64 y (sin.f64 (.f64 1/3 (.f64 t z))) (cos.f64 (.f64 1/3 (.f64 t z))))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (cbrt.f64 t) -1/3)) y))))
	44.1b	(fma.f64 a (/.f64 -1/3 b) (log.f64 (exp.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	26.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	17.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3)))) (cbrt.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))
	26.9b	(fma.f64 a (/.f64 1 (log1p.f64 (expm1.f64 (.f64 b -3)))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 (cbrt.f64 (.f64 t -1/3)) (cbrt.f64 (.f64 t -1/3))) (cbrt.f64 (*.f64 t -1/3))) y))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	30.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (*.f64 (pow.f64 t 3) -1/27)) y))))
	20.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	16.8b	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)) 3))))
	33.7b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	16.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	20.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cbrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))))
	35.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (expm1.f64 (log1p.f64 (*.f64 t -1/3))) y))))
	25.3b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
✓	16.8b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (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)))))
	17.2b	(fma.f64 a (.f64 (.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b)))) (cbrt.f64 (/.f64 1 b))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.1b	(*.f64 -1/3 (/.f64 a b))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.3b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3)) y))))
	29.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (sqrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (exp.f64 (log.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (.f64 1/3 (.f64 t z)))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (.f64 t -1/3)))))))
	20.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))

Compiler

Compiled 5367 to 3390 computations (36.8% saved)

regimes2.8s (26.3%)

Accuracy

Total 1.6b remaining (10.2%)

Threshold costs 0b (0%)

Counts

107 → 3

Compiler

Compiled 48860 to 36474 computations (25.3% saved)

bsearch5.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
5×	`+-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	41	104
1	58	104
2	67	104
3	73	104
4	77	104
5	78	104
6	76	104

end10.0ms (0.1%)

Compiler: Compiled 222 to 144 computations (35.1% saved)

sample4.3s (40.4%)

Algorithm

1×

intervals

Results

821.0ms	1575×	body	1024	valid
782.0ms	754×	body	2048	valid
456.0ms	4608×	body	128	valid
222.0ms	2281×	body	128	nan
214.0ms	739×	body	512	valid
107.0ms	1112×	body	128	invalid
77.0ms	324×	body	256	valid

Compiler

Compiled 987 to 723 computations (26.7% saved)

Details

analyze1.4s (13.5%)

sample166.0ms (1.6%)

simplify56.0ms (0.5%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series61.0ms (0.6%)

rewrite13.0ms (0.1%)

simplify139.0ms (1.3%)

prune241.0ms (2.3%)

localize9.0ms (0.1%)

series52.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify107.0ms (1%)

prune244.0ms (2.3%)

localize10.0ms (0.1%)

series38.0ms (0.4%)

rewrite8.0ms (0.1%)

simplify119.0ms (1.1%)

prune238.0ms (2.3%)

localize11.0ms (0.1%)

series42.0ms (0.4%)

rewrite13.0ms (0.1%)

simplify111.0ms (1.1%)

prune361.0ms (3.4%)

regimes2.8s (26.3%)

bsearch5.0ms (0%)

simplify6.0ms (0.1%)

end10.0ms (0.1%)

sample4.3s (40.4%)

Profiling