Details

analyze1.6s (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)

sample4.3s (36.9%)

Symmetry

(sort z t)

Results

1.2s	1622×	body	1024	valid
955.0ms	4765×	body	128	valid
794.0ms	715×	body	2048	valid
677.0ms	3580×	body	128	invalid
404.0ms	776×	body	512	valid
150.0ms	377×	body	256	valid
3.0ms	1×	body	4096	valid

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify61.0ms (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

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

23.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.2b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
▶	23.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))

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 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
✓	0.4b	(*.f64 t -1/3)
✓	0.4b	(/.f64 -1/3 b)
✓	25.6b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series55.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

42.0ms	(.f64 (.f64 2 (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 -1/3 b)
1.0ms	(*.f64 t -1/3)

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))

simplify143.0ms (1.2%)

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

prune229.0ms (2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	112	22	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	23	136

Error

14.8b

Counts

136 → 23

Alt Table

Status	Error	Program
	23.1b	(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))))
	32.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	23.2b	(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))))
	23.4b	(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))))
	30.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (fma.f64 (.f64 (cos.f64 y) (.f64 (.f64 t z) (.f64 t z))) -1/18 (fma.f64 1/3 (.f64 (sin.f64 y) (.f64 t z)) (cos.f64 y)))))
	23.2b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	23.2b	(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))))
	23.3b	(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)))))
	23.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log.f64 (exp.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	23.5b	(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))))))
	22.4b	(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)))))
	29.6b	(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))))))
	23.2b	(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))))
	23.2b	(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))))))
	50.0b	(fma.f64 a (/.f64 -1/3 b) (log.f64 (exp.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	41.0b	(fma.f64 a (.f64 (/.f64 1 (sqrt.f64 b)) (/.f64 -1/3 (sqrt.f64 b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))
	26.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (fma.f64 (cos.f64 y) 2 (.f64 (.f64 (sin.f64 y) (.f64 t z)) 2/3))))
	37.0b	(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))))))
	35.0b	(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))))))
	23.0b	(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))))
▶	17.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	36.0b	(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))))))
	22.4b	(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)))))))

Compiler

Compiled 4834 to 3080 computations (36.3% saved)

localize10.0ms (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)))
✓	0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
	0.4b	(/.f64 -1/3 b)

series54.0ms (0.5%)

Counts

2 → 49

Calls

2 calls:

36.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
18.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

rewrite7.0ms (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:

5.0ms	(.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)))

simplify88.0ms (0.8%)

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

prune241.0ms (2.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	7	15	22
Picked	1	0	1
Done	0	0	0
Total	96	25	121

Error

14.5b

Counts

121 → 25

Alt Table

Status	Error	Program
	23.1b	(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))))
	32.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	17.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (cbrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))))) (cbrt.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	23.2b	(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))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	23.4b	(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))))
	23.0b	(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))))
	37.0b	(*.f64 -1/3 (/.f64 a b))
	23.2b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	61.8b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	23.2b	(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))))
	17.6b	(fma.f64 a (.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 -1/3 (cbrt.f64 b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	36.0b	(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))))))
▶	17.2b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	23.3b	(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)))))
	26.0b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	23.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log.f64 (exp.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	17.2b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.4b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	22.4b	(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)))))))
	23.5b	(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))))))
	22.4b	(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)))))
	23.2b	(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))))))
	23.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 2 (sqrt.f64 x))) (.f64 2 (sqrt.f64 x))) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	37.0b	(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))))))

Compiler

Compiled 3148 to 1989 computations (36.8% saved)

localize10.0ms (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)))
	0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
✓	0.3b	(/.f64 b -1/3)
✓	0.6b	(/.f64 1 (/.f64 b -1/3))

series44.0ms (0.4%)

Counts

3 → 61

Calls

3 calls:

39.0ms	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
3.0ms	(/.f64 b -1/3)
2.0ms	(/.f64 1 (/.f64 b -1/3))

rewrite14.0ms (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)))

simplify115.0ms (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

prune358.0ms (3.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	220	24	244

Error

14.5b

Counts

244 → 24

Alt Table

Status	Error	Program
	23.1b	(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))))
	32.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	23.2b	(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))))
	23.4b	(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))))
▶	17.2b	(fma.f64 a (/.f64 1 (.f64 -3 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	23.0b	(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))))
	37.0b	(*.f64 -1/3 (/.f64 a b))
	23.2b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	61.8b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	23.2b	(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))))
	26.0b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	23.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log.f64 (exp.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	23.3b	(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)))))
	17.2b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.4b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	22.4b	(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)))))))
	23.5b	(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))))))
	22.4b	(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)))))
	37.0b	(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))))))
	29.1b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)))) (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 y))))))
	42.4b	(.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x)))
	36.0b	(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))))))
	23.2b	(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))))))
	23.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 2 (sqrt.f64 x))) (.f64 2 (sqrt.f64 x))) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 5784 to 3713 computations (35.8% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series41.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

39.0ms	(fma.f64 a (/.f64 1 (.f64 -3 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
2.0ms	(/.f64 1 (*.f64 -3 b))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(/.f64 1 (*.f64 -3 b))
0.0ms	(fma.f64 a (/.f64 1 (.f64 -3 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
533×	`times-frac_binary64`
381×	`cancel-sign-sub-inv_binary64`
332×	`fma-neg_binary64`
197×	`associate-*l/_binary64`

Counts

89 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1182
1	199	1055
2	488	1043
3	1450	1036
4	4187	1036
5	4908	1036

prune175.0ms (1.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	107	23	130

Error

14.5b

Counts

130 → 23

Alt Table

Status	Error	Program
	23.1b	(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))))
	32.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	23.2b	(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))))
	23.4b	(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))))
	23.0b	(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))))
	37.0b	(*.f64 -1/3 (/.f64 a b))
	23.2b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	61.8b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	23.2b	(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))))
	23.3b	(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)))))
	23.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (log.f64 (exp.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	17.2b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.4b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	22.4b	(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)))))))
	23.5b	(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))))))
	22.4b	(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)))))
	17.5b	(fma.f64 a (/.f64 1 (.f64 -3 b)) (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)))) (cbrt.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))) (cbrt.f64 (.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 y))))))
	42.4b	(.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x)))
	36.0b	(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))))))
	26.0b	(fma.f64 a (/.f64 1 (.f64 -3 b)) (.f64 2 (sqrt.f64 x)))
	23.2b	(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))))))
	23.8b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 2 (sqrt.f64 x))) (.f64 2 (sqrt.f64 x))) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	37.0b	(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))))))

Compiler

Compiled 2631 to 1645 computations (37.5% saved)

regimes3.4s (29%)

Accuracy

Total 1.6b remaining (10.2%)

Threshold costs 0b (0%)

Counts

124 → 3

Compiler

Compiled 60586 to 44895 computations (25.9% saved)

bsearch7.0ms (0.1%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	37	92
1	52	92
2	61	92
3	67	92
4	71	92
5	72	92
6	71	92

end607.0ms (5.2%)

Compiler: Compiled 908 to 656 computations (27.8% saved)

Details

analyze1.6s (13.5%)

sample4.3s (36.9%)

simplify61.0ms (0.5%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series55.0ms (0.5%)

rewrite13.0ms (0.1%)

simplify143.0ms (1.2%)

prune229.0ms (2%)

localize10.0ms (0.1%)

series54.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify88.0ms (0.8%)

prune241.0ms (2.1%)

localize10.0ms (0.1%)

series44.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify115.0ms (1%)

prune358.0ms (3.1%)

localize16.0ms (0.1%)

series41.0ms (0.4%)

rewrite5.0ms (0%)

simplify79.0ms (0.7%)

prune175.0ms (1.5%)

regimes3.4s (29%)

bsearch7.0ms (0.1%)

simplify5.0ms (0%)

end607.0ms (5.2%)

Profiling