Details

analyze1.4s (8.9%)

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
24.9%	74.8%	0.3%	7
24.9%	49.9%	25.2%	8
24.9%	49.9%	25.2%	9
24.9%	49.9%	25.2%	10
24.9%	49.9%	25.2%	11
24.9%	49.9%	25.2%	12
37.4%	37.4%	25.2%	13
37.4%	24.9%	37.7%	14

Compiler

Compiled 26 to 20 computations (23.1% saved)

sample4.7s (28.7%)

Symmetry

(sort z t)

Results

1.3s	1475×	body	1024	valid
1.2s	5127×	body	128	valid
1.0s	713×	body	2048	valid
469.0ms	2064×	body	128	invalid
351.0ms	646×	body	512	valid
136.0ms	291×	body	256	valid
10.0ms	4×	body	4096	valid

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify119.0ms (0.7%)

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

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

21.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
▶	21.4b	(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)

localize29.0ms (0.2%)

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)
✓	24.1b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series95.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

67.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
21.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))
3.0ms	(*.f64 t -1/3)
3.0ms	(/.f64 -1/3 b)

rewrite15.0ms (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:

6.0ms	(.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))

simplify212.0ms (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

prune313.0ms (1.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	116	18	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	19	136

Error

15.6b

Counts

136 → 19

Alt Table

Status	Error	Program
	35.4b	(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))))))
	33.6b	(fma.f64 a (expm1.f64 (log1p.f64 (/.f64 -1/3 b))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	28.6b	(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)))))
	21.9b	(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))))
	21.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (.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))))))
	31.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) -1/3)) y))))
▶	17.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	53.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 (.f64 t -1/3)) (sqrt.f64 (*.f64 t -1/3))) y))))
	21.5b	(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)))))))
	21.6b	(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))))
	21.3b	(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)))))
	21.5b	(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)))))
	21.4b	(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))))))
	42.6b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))
	21.6b	(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))))
	21.7b	(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))))))
	27.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	21.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.6b	(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))))

Compiler

Compiled 4600 to 2900 computations (37% 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)))
✓	0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
	0.4b	(/.f64 -1/3 b)

series62.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

42.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
20.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

rewrite10.0ms (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))
1.0ms	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify135.0ms (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

prune267.0ms (1.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	93	24	117

Error

15.2b

Counts

117 → 24

Alt Table

Status	Error	Program
	21.7b	(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))))))
	40.2b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.4b	(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))))))
	28.6b	(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)))))
	18.2b	(.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)))))
	21.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.9b	(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))))
	21.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (.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))))))
	31.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) -1/3)) y))))
	34.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	53.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 (.f64 t -1/3)) (sqrt.f64 (*.f64 t -1/3))) y))))
	21.5b	(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)))))))
	21.6b	(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))))
	21.3b	(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)))))
	28.4b	(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)))))
	21.5b	(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)))))
	21.4b	(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))))))
	22.0b	(fma.f64 a (/.f64 -1/3 b) (expm1.f64 (log1p.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	31.8b	(*.f64 -1/3 (/.f64 a b))
	27.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	23.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
▶	17.7b	(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))))
	21.6b	(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))))
	44.0b	(log1p.f64 (expm1.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))

Compiler

Compiled 3196 to 1989 computations (37.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series939.0ms (5.8%)

Counts

3 → 36

Calls

3 calls:

417.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
312.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
209.0ms	(cbrt.f64 (cos.f64 y))

rewrite20.0ms (0.1%)

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:

10.0ms	(.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))

simplify164.0ms (1%)

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

prune771.0ms (4.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	195	6	201
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	197	28	225

Error

15.1b

Counts

225 → 28

Alt Table

Status	Error	Program
	21.7b	(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))))))
	40.2b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	17.9b	(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))))
	23.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	18.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (exp.f64 (log.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
	35.4b	(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))))))
	28.6b	(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)))))
	18.2b	(.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)))))
	21.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.9b	(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))))
	21.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (.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))))))
	31.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) -1/3)) y))))
	34.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (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)) (cbrt.f64 (cos.f64 y))))
	21.6b	(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))))
	53.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 (.f64 t -1/3)) (sqrt.f64 (*.f64 t -1/3))) y))))
	21.5b	(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)))))))
▶	17.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	21.6b	(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))))
	21.3b	(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)))))
	28.4b	(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)))))
	23.2b	(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))))
	21.5b	(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)))))
	21.4b	(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))))))
	31.8b	(*.f64 -1/3 (/.f64 a b))
	27.5b	(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 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) 1))
	44.0b	(log1p.f64 (expm1.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))

Compiler

Compiled 6992 to 3432 computations (50.9% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series322.0ms (2%)

Counts

2 → 16

Calls

2 calls:

315.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
6.0ms	(pow.f64 (cos.f64 y) 2)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
15×	`prod-exp_binary64`
14×	`unpow-prod-down_binary64`
12×	`associate-r_binary64`
10×	`add-cbrt-cube_binary64`

Counts

2 → 57

Calls

2 calls:

8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-neg_binary64`
634×	`unswap-sqr_binary64`
537×	`fma-def_binary64`
352×	`*-commutative_binary64`
313×	`log-prod_binary64`

Counts

73 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1180
1	307	990
2	968	970
3	1811	963
4	4207	963
5	5103	963

prune492.0ms (3%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	3	24	27
Picked	0	1	1
Done	0	0	0
Total	145	29	174

Error

15.1b

Counts

174 → 29

Alt Table

Status	Error	Program
	21.7b	(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))))))
	40.2b	(fma.f64 a (/.f64 (/.f64 -1/3 (sqrt.f64 b)) (sqrt.f64 b)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	17.9b	(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))))
	18.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (exp.f64 (log.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)))) (cbrt.f64 (cos.f64 y))))
	27.5b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	35.4b	(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))))))
	28.6b	(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)))))
	18.2b	(.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)))))
	21.4b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.9b	(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))))
	21.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (.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))))))
	31.7b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) -1/3)) y))))
	34.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))) (fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))) (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)) (cbrt.f64 (cos.f64 y))))
	21.6b	(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))))
	53.9b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 (sqrt.f64 (.f64 t -1/3)) (sqrt.f64 (*.f64 t -1/3))) y))))
	21.5b	(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)))))))
✓	17.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	21.6b	(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))))
	21.3b	(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)))))
	28.4b	(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)))))
	23.2b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) 1))
	21.5b	(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)))))
	21.4b	(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))))))
	21.6b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cbrt.f64 (cos.f64 y))) (pow.f64 (sqrt.f64 (pow.f64 (cos.f64 y) 2)) 1/3)) (cbrt.f64 (cos.f64 y))))
	17.8b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (.f64 2 (.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))))) (cbrt.f64 (.f64 2 (*.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))))) (cbrt.f64 (cos.f64 y))))
	31.8b	(*.f64 -1/3 (/.f64 a b))
	23.1b	(fma.f64 a (/.f64 -1/3 b) (*.f64 2 (sqrt.f64 x)))
	44.0b	(log1p.f64 (expm1.f64 (fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))))

Compiler

Compiled 4697 to 2887 computations (38.5% saved)

regimes5.1s (31.4%)

Accuracy

Total 1.9b remaining (12.9%)

Threshold costs 0b (0%)

Counts

149 → 3

Compiler

Compiled 70588 to 49756 computations (29.5% saved)

bsearch239.0ms (1.5%)

Steps

Iters	Range		Point
5	5.503022827831678e+307	#hash((type . real) (value . +inf))	1.7727566483509542e+308
6	#hash((type . real) (value . -inf))	-1.6628757877770306e+307	-1.7729749144956428e+308

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	74
1	40	74
2	52	74
3	66	74
4	76	74
5	82	74
6	84	74
7	84	74

end624.0ms (3.8%)

Remove: (sort z t)
Compiler: Compiled 1131 to 798 computations (29.4% saved)

Details

analyze1.4s (8.9%)

sample4.7s (28.7%)

simplify119.0ms (0.7%)

prune9.0ms (0.1%)

localize29.0ms (0.2%)

series95.0ms (0.6%)

rewrite15.0ms (0.1%)

simplify212.0ms (1.3%)

prune313.0ms (1.9%)

localize10.0ms (0.1%)

series62.0ms (0.4%)

rewrite10.0ms (0.1%)

simplify135.0ms (0.8%)

prune267.0ms (1.6%)

localize13.0ms (0.1%)

series939.0ms (5.8%)

rewrite20.0ms (0.1%)

simplify164.0ms (1%)

prune771.0ms (4.8%)

localize55.0ms (0.3%)

series322.0ms (2%)

rewrite13.0ms (0.1%)

simplify105.0ms (0.6%)

prune492.0ms (3%)

regimes5.1s (31.4%)

bsearch239.0ms (1.5%)

simplify7.0ms (0%)

end624.0ms (3.8%)

Profiling