Details

analyze1.7s (11.4%)

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)

sample4.4s (30%)

Symmetry

(sort z t)

Results

1.3s	1663×	body	1024	valid
978.0ms	4813×	body	128	valid
836.0ms	733×	body	2048	valid
662.0ms	3457×	body	128	invalid
371.0ms	695×	body	512	valid
121.0ms	349×	body	256	valid
7.0ms	3×	body	4096	valid

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify59.0ms (0.4%)

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

19.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	19.9b	(-.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)

localize15.0ms (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 -1/3 b)
✓	0.4b	(*.f64 t -1/3)
✓	22.6b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series53.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

40.0ms	(.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 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))

simplify145.0ms (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

prune225.0ms (1.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	114	19	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	20	135

Error

13.8b

Counts

135 → 20

Alt Table

Status	Error	Program
	19.6b	(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))))
	36.5b	(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))))))
	27.1b	(fma.f64 a (/.f64 -1/3 b) (expm1.f64 (log1p.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.0b	(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))))
	31.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	19.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	20.2b	(fma.f64 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))))
	28.5b	(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 (fma.f64 z (.f64 t -1/3) y)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.5b	(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)))))))
	34.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (sqrt.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))))
	20.2b	(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)) (expm1.f64 (log1p.f64 (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
▶	16.3b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.7b	(fma.f64 a (cbrt.f64 (.f64 (.f64 (/.f64 -1/3 b) (/.f64 -1/3 b)) (/.f64 -1/3 b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (+.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (.f64 2/3 (.f64 (.f64 (sin.f64 y) (.f64 t z)) (sqrt.f64 x)))))
	19.5b	(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))))
	20.1b	(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)) (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))))
	20.2b	(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 (fma.f64 z (*.f64 t -1/3) y))))
	54.5b	(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))))

Compiler

Compiled 4653 to 2951 computations (36.6% saved)

localize12.0ms (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)

series53.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

38.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
15.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

rewrite6.0ms (0%)

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)))

simplify94.0ms (0.6%)

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

prune184.0ms (1.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	92	26	118

Error

13.4b

Counts

118 → 26

Alt Table

Status	Error	Program
	31.7b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.5b	(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))))
	19.6b	(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))))
	36.5b	(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))))))
	34.4b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
▶	16.3b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.1b	(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))))))
	27.1b	(fma.f64 a (/.f64 -1/3 b) (expm1.f64 (log1p.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.0b	(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))))
	16.7b	(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)))
	41.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	31.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	39.4b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 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)) (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))))
	19.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	29.5b	(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)))))
	28.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	28.5b	(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 (fma.f64 z (.f64 t -1/3) y)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.5b	(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)))))))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (+.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (.f64 2/3 (.f64 (.f64 (sin.f64 y) (.f64 t z)) (sqrt.f64 x)))))
	37.4b	(*.f64 -1/3 (/.f64 a b))
	16.6b	(fma.f64 a (.f64 (/.f64 (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 b))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	16.6b	(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)))))
	19.9b	(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))))))
	61.6b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	54.5b	(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))))

Compiler

Compiled 3154 to 1995 computations (36.7% saved)

localize11.0ms (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))

series35.0ms (0.2%)

Counts

2 → 49

Calls

2 calls:

33.0ms	(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))

rewrite9.0ms (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))
2.0ms	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify110.0ms (0.7%)

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

prune196.0ms (1.3%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	25	25
Picked	0	1	1
Done	0	0	0
Total	121	26	147

Error

13.4b

Counts

147 → 26

Alt Table

Status	Error	Program
	31.7b	(expm1.f64 (log1p.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.5b	(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))))
	19.6b	(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))))
	36.5b	(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))))))
	34.4b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
✓	16.3b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.1b	(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))))))
	27.1b	(fma.f64 a (/.f64 -1/3 b) (expm1.f64 (log1p.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.0b	(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))))
	16.7b	(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)))
	41.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	31.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	39.4b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 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)) (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))))
	19.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	29.5b	(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)))))
	28.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	28.5b	(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 (fma.f64 z (.f64 t -1/3) y)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	19.5b	(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)))))))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (+.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (.f64 2/3 (.f64 (.f64 (sin.f64 y) (.f64 t z)) (sqrt.f64 x)))))
	37.4b	(*.f64 -1/3 (/.f64 a b))
	16.6b	(fma.f64 a (.f64 (/.f64 (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 b))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
▶	16.6b	(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)))))
	19.9b	(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))))))
	61.6b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	54.5b	(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))))

Compiler

Compiled 3742 to 2410 computations (35.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
	0.3b	(/.f64 -1/3 b)
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))))
✓	0.6b	(cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

series1.1s (7.7%)

Counts

3 → 52

Calls

3 calls:

592.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))))

502.0ms

(cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))

31.0ms

(*.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))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms

(*.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))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))))

3.0ms

(cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
608×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
361×	`fma-def_binary64`
278×	`cancel-sign-sub-inv_binary64`

Counts

131 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	2762
1	364	2420
2	1266	2108
3	2981	1978
4	5057	1978

prune417.0ms (2.8%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	216	10	226
Fresh	3	21	24
Picked	1	0	1
Done	0	1	1
Total	220	32	252

Error

13.3b

Counts

252 → 32

Alt Table

Status	Error	Program
	34.1b	(fma.f64 a (/.f64 -1/3 b) (pow.f64 (.f64 8 (pow.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) 3)) 1/3))
	19.5b	(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))))
	19.6b	(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))))
	36.5b	(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))))))
	34.4b	(fma.f64 a (cbrt.f64 (pow.f64 (/.f64 -1/3 b) 3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
✓	16.3b	(fma.f64 a (.f64 -1/3 (/.f64 1 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	20.1b	(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))))))
	27.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (pow.f64 (cbrt.f64 2) 2) (cbrt.f64 x)) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	27.1b	(fma.f64 a (/.f64 -1/3 b) (expm1.f64 (log1p.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.0b	(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))))
	16.7b	(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)))
	31.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	39.4b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 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)) (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))))
	17.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (exp.f64 (.f64 1/3 (+.f64 (log.f64 x) (log.f64 (pow.f64 (cos.f64 y) 2))))) (pow.f64 (cbrt.f64 2) 2)) (cbrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	41.5b	(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)))) (.f64 (+.f64 (.f64 (.f64 y y) -1/6) 1) (.f64 (cbrt.f64 2) (pow.f64 x 1/6)))))
	17.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (pow.f64 (.f64 4 (.f64 x (pow.f64 (cos.f64 y) 2))) 1/3) (cbrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	19.5b	(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)))))))
	28.5b	(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 (fma.f64 z (.f64 t -1/3) y)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	16.6b	(fma.f64 a (.f64 (/.f64 (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 b))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	16.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (sqrt.f64 x))) (cbrt.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)) (cos.f64 y)))))
	19.9b	(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))))))
	28.4b	(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)))) (*.f64 (cbrt.f64 2) (pow.f64 x 1/6))))
	54.5b	(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))))
	30.5b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))))) (log.f64 (cbrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))))))
	16.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (.f64 (cbrt.f64 (.f64 2 (sqrt.f64 x))) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (+.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (.f64 2/3 (.f64 (.f64 (sin.f64 y) (.f64 t z)) (sqrt.f64 x)))))
	37.4b	(*.f64 -1/3 (/.f64 a b))
	17.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (cos.f64 y) (.f64 2 (sqrt.f64 x))))) 8) (cbrt.f64 (cbrt.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y))))))
	61.6b	(log.f64 (exp.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))

Compiler

Compiled 8922 to 5486 computations (38.5% saved)

regimes5.0s (33.9%)

Accuracy

Total 1.8b remaining (11.1%)

Threshold costs 0b (0%)

Counts

169 → 3

Compiler

Compiled 90807 to 66546 computations (26.7% saved)

bsearch8.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-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	43	110
1	58	110
2	68	110
3	74	110
4	78	110
5	79	110
6	79	110

end698.0ms (4.8%)

Remove: (sort z t)
Compiler: Compiled 1253 to 910 computations (27.4% saved)

Details

analyze1.7s (11.4%)

sample4.4s (30%)

simplify59.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series53.0ms (0.4%)

rewrite13.0ms (0.1%)

simplify145.0ms (1%)

prune225.0ms (1.5%)

localize12.0ms (0.1%)

series53.0ms (0.4%)

rewrite6.0ms (0%)

simplify94.0ms (0.6%)

prune184.0ms (1.3%)

localize11.0ms (0.1%)

series35.0ms (0.2%)

rewrite9.0ms (0.1%)

simplify110.0ms (0.7%)

prune196.0ms (1.3%)

localize15.0ms (0.1%)

series1.1s (7.7%)

rewrite23.0ms (0.2%)

simplify91.0ms (0.6%)

prune417.0ms (2.8%)

regimes5.0s (33.9%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end698.0ms (4.8%)

Profiling