Details

analyze1.4s (10.7%)

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)

sample183.0ms (1.4%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

23.0ms	53×	body	1024	valid
20.0ms	26×	body	2048	valid
17.0ms	143×	body	128	valid
10.0ms	75×	body	128	nan
7.0ms	24×	body	512	valid
3.0ms	32×	body	128	invalid
2.0ms	9×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify62.0ms (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

19.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	19.8b	(-.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)))
✓	0.4b	(/.f64 -1/3 b)
✓	0.4b	(*.f64 t -1/3)
✓	26.8b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series58.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

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

rewrite16.0ms (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:

7.0ms	(.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))

simplify146.0ms (1.1%)

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 → 133

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

prune222.0ms (1.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	111	22	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	23	135

Error

14.8b

Counts

135 → 23

Alt Table

Status	Error	Program
	19.7b	(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))))
	19.7b	(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))))))
	20.0b	(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))))))
	19.9b	(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))))
	49.6b	(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))))))
	19.9b	(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))))
	36.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (log.f64 (exp.f64 (*.f64 t -1/3))) y))))
	28.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	19.8b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	19.7b	(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))))
	19.7b	(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))))
	34.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (sqrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (sqrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.0b	(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))))
	19.7b	(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))))))
▶	17.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	19.0b	(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)))))))
	19.2b	(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)))))
	19.8b	(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)))))
	35.4b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (.f64 (.f64 (.f64 t -1/3) (.f64 t -1/3)) (*.f64 t -1/3))) y))))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (.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))))))
	19.7b	(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))))
	34.9b	(fma.f64 a (cbrt.f64 (/.f64 (.f64 (.f64 -1/3 -1/3) -1/3) (.f64 (.f64 b b) b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))

Compiler

Compiled 4793 to 3073 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))
	0.4b	(/.f64 -1/3 b)

series47.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

30.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
16.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

rewrite9.0ms (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:

7.0ms	(.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)))

simplify94.0ms (0.7%)

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

prune198.0ms (1.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	7	15	22
Picked	1	0	1
Done	0	0	0
Total	94	27	121

Error

14.4b

Counts

121 → 27

Alt Table

Status	Error	Program
	26.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	19.2b	(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)))))
▶	17.8b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	17.9b	(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))))
	19.7b	(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))))
	19.7b	(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))))))
	20.0b	(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))))))
	19.9b	(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))))
	35.1b	(.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)))))
	19.9b	(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))))
	37.2b	(exp.f64 (log.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (.f64 (.f64 (.f64 t -1/3) (.f64 t -1/3)) (*.f64 t -1/3))) y))))
	62.3b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	28.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	18.2b	(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 y)))
	34.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (sqrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (sqrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	37.1b	(*.f64 -1/3 (/.f64 a b))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (.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))))))
	33.4b	(fma.f64 a (cbrt.f64 (/.f64 (.f64 (.f64 -1/3 -1/3) -1/3) (.f64 (.f64 b b) b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.1b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.7b	(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))))
	35.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	19.7b	(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))))))
	19.0b	(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)))))))
	18.2b	(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)))))
	35.4b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))
	19.8b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))

Compiler

Compiled 3248 to 2065 computations (36.4% 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))
✓	0.4b	(*.f64 -1/3 (/.f64 1 b))

series37.0ms (0.3%)

Counts

2 → 49

Calls

2 calls:

35.0ms	(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))

rewrite12.0ms (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)))

simplify121.0ms (0.9%)

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

prune208.0ms (1.6%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	26	26
Picked	0	1	1
Done	0	0	0
Total	121	27	148

Error

14.4b

Counts

148 → 27

Alt Table

Status	Error	Program
	26.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	19.2b	(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)))))
✓	17.8b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
▶	17.9b	(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))))
	19.7b	(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))))
	19.7b	(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))))))
	20.0b	(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))))))
	19.9b	(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))))
	35.1b	(.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)))))
	19.9b	(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))))
	37.2b	(exp.f64 (log.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (.f64 (.f64 (.f64 t -1/3) (.f64 t -1/3)) (*.f64 t -1/3))) y))))
	62.3b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	28.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	18.2b	(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 y)))
	34.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (sqrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (sqrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	37.1b	(*.f64 -1/3 (/.f64 a b))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (.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))))))
	33.4b	(fma.f64 a (cbrt.f64 (/.f64 (.f64 (.f64 -1/3 -1/3) -1/3) (.f64 (.f64 b b) b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.1b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.7b	(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))))
	35.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	19.7b	(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))))))
	19.0b	(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)))))))
	18.2b	(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)))))
	35.4b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))
	19.8b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))

Compiler

Compiled 3836 to 2480 computations (35.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series664.0ms (5.1%)

Counts

3 → 36

Calls

3 calls:

250.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
242.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
171.0ms	(cbrt.f64 (cos.f64 y))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 79

Calls

3 calls:

19.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

505×	`sub-neg_binary64`
427×	`unswap-sqr_binary64`
406×	`*-commutative_binary64`
369×	`fma-neg_binary64`
322×	`log-prod_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1618
1	300	1343
2	1040	1267
3	2065	1249
4	4501	1129
5	4502	1129
6	5086	1129

prune455.0ms (3.5%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	192	9	201
Fresh	4	21	25
Picked	1	0	1
Done	0	1	1
Total	197	31	228

Error

14.4b

Counts

228 → 31

Alt Table

Status	Error	Program
	35.6b	(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)))) (fma.f64 (*.f64 y y) -1/6 1)))
✓	17.8b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	26.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	19.2b	(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)))))
	19.7b	(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))))
	19.7b	(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))))))
	17.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (exp.f64 (log.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
	26.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) 1)) (cbrt.f64 (cos.f64 y))))
	26.0b	(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)))) 1))
	20.0b	(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))))))
	19.9b	(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))))
	18.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
	35.1b	(.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)))))
	19.9b	(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))))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (cbrt.f64 (.f64 8 (.f64 (pow.f64 (cos.f64 y) 2) (.f64 x (sqrt.f64 x))))) (cbrt.f64 (cos.f64 y))))
	35.4b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y))))))
	19.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (exp.f64 (+.f64 (log.f64 (.f64 2 (sqrt.f64 x))) (log.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
	37.2b	(exp.f64 (log.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (cbrt.f64 (.f64 (.f64 (.f64 t -1/3) (.f64 t -1/3)) (*.f64 t -1/3))) y))))
	62.3b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	28.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	37.1b	(*.f64 -1/3 (/.f64 a b))
	19.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (.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))))))
	33.4b	(fma.f64 a (cbrt.f64 (/.f64 (.f64 (.f64 -1/3 -1/3) -1/3) (.f64 (.f64 b b) b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	33.1b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.7b	(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))))
	19.0b	(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)))))))
	19.8b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	18.2b	(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 y)))
	25.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (cos.f64 y))))
	18.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 6166 to 2860 computations (53.6% saved)

regimes4.7s (36%)

Accuracy

Total 1.8b remaining (10.9%)

Threshold costs 0b (0%)

Counts

139 → 3

Compiler

Compiled 70704 to 50705 computations (28.3% saved)

bsearch7.0ms (0.1%)

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

simplify6.0ms (0%)

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	39	94
1	53	94
2	63	94
3	69	94
4	73	94
5	74	94
6	74	94

end13.0ms (0.1%)

Compiler: Compiled 204 to 129 computations (36.8% saved)

sample4.2s (32.1%)

Algorithm

1×

intervals

Results

901.0ms	1647×	body	1024	valid
602.0ms	709×	body	2048	valid
484.0ms	4585×	body	128	valid
261.0ms	724×	body	512	valid
227.0ms	2244×	body	128	nan
109.0ms	1138×	body	128	invalid
71.0ms	333×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 988 to 707 computations (28.4% saved)

Details

analyze1.4s (10.7%)

sample183.0ms (1.4%)

simplify62.0ms (0.5%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series58.0ms (0.4%)

rewrite16.0ms (0.1%)

simplify146.0ms (1.1%)

prune222.0ms (1.7%)

localize9.0ms (0.1%)

series47.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify94.0ms (0.7%)

prune198.0ms (1.5%)

localize10.0ms (0.1%)

series37.0ms (0.3%)

rewrite12.0ms (0.1%)

simplify121.0ms (0.9%)

prune208.0ms (1.6%)

localize14.0ms (0.1%)

series664.0ms (5.1%)

rewrite28.0ms (0.2%)

simplify113.0ms (0.9%)

prune455.0ms (3.5%)

regimes4.7s (36%)

bsearch7.0ms (0.1%)

simplify6.0ms (0%)

end13.0ms (0.1%)

sample4.2s (32.1%)

Profiling