Details

analyze1.3s (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)

sample184.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

28.0ms	61×	body	1024	valid
19.0ms	143×	body	128	valid
18.0ms	22×	body	2048	valid
8.0ms	20×	body	512	valid
6.0ms	63×	body	128	nan
4.0ms	42×	body	128	invalid
3.0ms	10×	body	256	valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify55.0ms (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

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

20.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
▶	20.8b	(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
✓	0.3b	(.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)
✓	21.3b	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

series53.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

39.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
11.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))
1.0ms	(*.f64 t -1/3)
1.0ms	(/.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:

7.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y)))
2.0ms	(*.f64 t -1/3)
2.0ms	(/.f64 -1/3 b)
1.0ms	(cos.f64 (fma.f64 z (*.f64 t -1/3) y))

simplify131.0ms (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 (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	108	25	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	109	26	135

Error

15.1b

Counts

135 → 26

Alt Table

Status	Error	Program
	27.2b	(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))))))
	20.9b	(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))))
	21.2b	(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))))
	20.9b	(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))))
	20.8b	(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))))
	32.7b	(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))))))
	55.7b	(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))))
	28.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	20.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	28.2b	(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)))))
	20.9b	(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)))))
	37.3b	(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))))
	20.8b	(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 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	21.1b	(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))))))
	21.2b	(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))))
	20.4b	(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)))))))
	29.4b	(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))))
	20.9b	(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))))
	41.8b	(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))))
	34.9b	(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)))))
	21.2b	(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 (fma.f64 z (.f64 t -1/3) y))))
	35.0b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (sqrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	28.1b	(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))))))
	20.4b	(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)))))
	46.2b	(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))))))

Compiler

Compiled 5049 to 3231 computations (36% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series49.0ms (0.4%)

Counts

2 → 49

Calls

2 calls:

33.0ms	(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))

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:

4.0ms	(.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 (0.7%)

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

prune179.0ms (1.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	10	15	25
Picked	1	0	1
Done	0	0	0
Total	95	29	124

Error

14.7b

Counts

124 → 29

Alt Table

Status	Error	Program
	20.9b	(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))))
	17.7b	(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)))
	20.9b	(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))))
	35.4b	(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)))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	24.8b	(fma.f64 2 (sqrt.f64 x) (*.f64 (/.f64 a b) -1/3))
	32.7b	(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))))))
	17.3b	(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))))
	55.7b	(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))))
	28.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	20.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	17.2b	(fma.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (/.f64 a b) -1/3))
	28.2b	(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)))))
▶	17.2b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	37.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	17.7b	(fma.f64 a (/.f64 (/.f64 -1/3 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	17.5b	(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)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	28.1b	(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))))))
	20.8b	(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))))))
	21.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.4b	(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)))))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (*.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 y)))))
	20.4b	(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)))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (log.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	20.9b	(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))))
	29.4b	(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))))
	35.5b	(*.f64 -1/3 (/.f64 a b))
	21.2b	(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 (fma.f64 z (.f64 t -1/3) y))))

Compiler

Compiled 3364 to 2129 computations (36.7% 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)))
	0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
✓	0.3b	(/.f64 1 (/.f64 b -1/3))
✓	0.3b	(/.f64 b -1/3)

series39.0ms (0.3%)

Counts

3 → 61

Calls

3 calls:

35.0ms	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
2.0ms	(/.f64 b -1/3)
1.0ms	(/.f64 1 (/.f64 b -1/3))

rewrite15.0ms (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:

7.0ms	(/.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)))

simplify108.0ms (0.9%)

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 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2397
1	277	2076
2	623	2035
3	1599	2028
4	4483	2028
5	4985	2028

prune351.0ms (2.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	7	21	28
Picked	1	0	1
Done	0	0	0
Total	218	28	246

Error

14.7b

Counts

246 → 28

Alt Table

Status	Error	Program
	20.9b	(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))))
	17.2b	(fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))))
	29.4b	(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))))
	17.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))))) (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x)))))) (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))))))
	20.9b	(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))))
	35.4b	(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)))
	29.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	32.7b	(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))))))
	17.3b	(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))))
▶	17.2b	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.5b	(*.f64 -1/3 (/.f64 a b))
	55.7b	(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))))
	28.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	37.1b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y))))
	20.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	17.6b	(fma.f64 a (/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 b -1/3)) (cbrt.f64 (/.f64 b -1/3))) (cbrt.f64 (/.f64 b -1/3)))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	28.1b	(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))))))
	20.8b	(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))))))
	21.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.4b	(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)))))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (*.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 y)))))
	20.9b	(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))))
	28.2b	(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)))))
	21.2b	(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 (fma.f64 z (.f64 t -1/3) y))))
	29.9b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (exp.f64 (log.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	20.4b	(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)))))
	24.8b	(fma.f64 -1/3 (/.f64 a b) (*.f64 2 (sqrt.f64 x)))

Compiler

Compiled 6045 to 3885 computations (35.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series34.0ms (0.3%)

Counts

2 → 49

Calls

2 calls:

33.0ms	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
1.0ms	(/.f64 (/.f64 1 b) (/.f64 1 -1/3))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

421×	`times-frac_binary64`
198×	`*-un-lft-identity_binary64`
198×	`add-sqr-sqrt_binary64`
198×	`add-cube-cbrt_binary64`
42×	`add-exp-log_binary64`

Counts

2 → 239

Calls

2 calls:

8.0ms	(/.f64 (/.f64 1 b) (/.f64 1 -1/3))
0.0ms	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))

simplify198.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-neg_binary64`
640×	`fma-def_binary64`
441×	`associate-/l*_binary64`
414×	`cancel-sign-sub-inv_binary64`
236×	`associate-*l/_binary64`

Counts

288 → 289

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	4916
1	374	4228
2	874	4066
3	2025	4059
4	4317	4057
5	4740	4057
6	4911	4057

prune490.0ms (3.9%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	320	4	324
Fresh	4	23	27
Picked	0	1	1
Done	0	0	0
Total	324	28	352

Error

14.7b

Counts

352 → 28

Alt Table

Status	Error	Program
	29.4b	(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))))
	17.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))))) (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x)))))) (cbrt.f64 (fma.f64 -1/3 (/.f64 a b) (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))))))
	20.9b	(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))))
	44.1b	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (log.f64 (exp.f64 (.f64 2 (.f64 (sqrt.f64 x) (cos.f64 y))))))
	20.9b	(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 (.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	32.7b	(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))))))
	17.3b	(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))))
✓	17.2b	(fma.f64 a (/.f64 (/.f64 1 b) (/.f64 1 -1/3)) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	35.5b	(*.f64 -1/3 (/.f64 a b))
	55.7b	(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))))
	28.4b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (.f64 1/3 (.f64 t z)))))
	20.9b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
	21.2b	(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 (fma.f64 z (.f64 t -1/3) y))))
	17.3b	(fma.f64 a (/.f64 (/.f64 (/.f64 1 b) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 (/.f64 1 -1/3))) (.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	25.2b	(fma.f64 a (/.f64 -1/3 b) (cbrt.f64 (.f64 8 (pow.f64 (.f64 (sqrt.f64 x) (cos.f64 y)) 3))))
	28.1b	(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))))))
	20.8b	(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))))))
	21.1b	(fma.f64 a (/.f64 -1/3 b) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y)))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (.f64 t -1/3) y))))) (cbrt.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))))))
	20.4b	(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)))))))
	30.0b	(fma.f64 a (/.f64 -1/3 b) (exp.f64 (+.f64 (log.f64 (*.f64 2 (sqrt.f64 x))) (log.f64 (cos.f64 y)))))
	24.8b	(fma.f64 -1/3 (/.f64 a b) (*.f64 2 (sqrt.f64 x)))
	37.1b	(fma.f64 (sqrt.f64 x) (-.f64 2 (.f64 y y)) (.f64 -1/3 (/.f64 a b)))
	20.9b	(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))))
	17.2b	(fma.f64 a (.f64 (/.f64 1 (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (/.f64 (/.f64 1 b) (cbrt.f64 -3))) (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))
	28.2b	(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)))))
	29.9b	(fma.f64 a (/.f64 1 (/.f64 b -1/3)) (exp.f64 (log.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)))))
	20.4b	(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)))))

Compiler

Compiled 9307 to 6468 computations (30.5% saved)

regimes4.8s (38.6%)

Accuracy

Total 1.9b remaining (11.4%)

Threshold costs 0b (0%)

Counts

172 → 3

Compiler

Compiled 78490 to 59492 computations (24.2% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	98
1	64	98
2	78	98
3	94	98
4	105	98
5	111	98
6	113	98
7	111	98

end9.0ms (0.1%)

Compiler: Compiled 210 to 141 computations (32.9% saved)

sample4.0s (32%)

Algorithm

1×

intervals

Results

940.0ms	1580×	body	1024	valid
610.0ms	735×	body	2048	valid
445.0ms	4593×	body	128	valid
353.0ms	749×	body	512	valid
234.0ms	2294×	body	128	nan
109.0ms	1100×	body	128	invalid
80.0ms	341×	body	256	valid
5.0ms	2×	body	4096	valid

Compiler

Compiled 907 to 664 computations (26.8% saved)

Details

analyze1.3s (10.7%)

sample184.0ms (1.5%)

simplify55.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series53.0ms (0.4%)

rewrite15.0ms (0.1%)

simplify131.0ms (1.1%)

prune222.0ms (1.8%)

localize9.0ms (0.1%)

series49.0ms (0.4%)

rewrite6.0ms (0%)

simplify88.0ms (0.7%)

prune179.0ms (1.4%)

localize10.0ms (0.1%)

series39.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify108.0ms (0.9%)

prune351.0ms (2.8%)

localize12.0ms (0.1%)

series34.0ms (0.3%)

rewrite33.0ms (0.3%)

simplify198.0ms (1.6%)

prune490.0ms (3.9%)

regimes4.8s (38.6%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end9.0ms (0.1%)

sample4.0s (32%)

Profiling