Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample4.6s (39.2%)

Results

2.5s	2040×	body	1024	valid
1.1s	4603×	body	128	valid
705.0ms	1097×	body	512	valid
221.0ms	512×	body	256	valid
9.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
✓	0.1b	(*.f64 x (cos.f64 y))
✓	0.1b	(*.f64 z (sin.f64 y))

series60.0ms (0.5%)

Counts

4 → 88

Calls

4 calls:

31.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
13.0ms	(*.f64 z (sin.f64 y))
12.0ms	(*.f64 x (cos.f64 y))
3.0ms	(cos.f64 y)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 65

Calls

4 calls:

9.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
6.0ms	(*.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

simplify146.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
542×	`fma-def_binary64`
292×	`cancel-sign-sub-inv_binary64`
289×	`distribute-rgt-neg-in_binary64`
255×	`*-commutative_binary64`

Counts

153 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1664
1	369	1608
2	1136	1575
3	2483	1575
4	4571	1575
5	4907	1575

prune183.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

0.0b

Counts

128 → 10

Alt Table

Status	Error	Program
	32.5b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	29.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	27.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
	25.8b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	31.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	32.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 2308 to 790 computations (65.8% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.4b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series40.0ms (0.3%)

Counts

3 → 40

Calls

3 calls:

25.0ms	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
12.0ms	(pow.f64 (cos.f64 y) 3)
4.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

12.0ms	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
3.0ms	(pow.f64 (cos.f64 y) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

simplify169.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-neg_binary64`
630×	`fma-def_binary64`
330×	`sqr-pow_binary64`
300×	`*-commutative_binary64`
260×	`cancel-sign-sub-inv_binary64`

Counts

124 → 126

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	1089
1	251	1015
2	841	981
3	1741	975
4	3601	972
5	4788	972
6	4933	972

prune303.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	25.8b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))
	31.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	32.5b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	29.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
▶	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	27.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	32.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 3188 to 1549 computations (51.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(*.f64 (cos.f64 y) (cos.f64 y))
✓	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))

series818.0ms (6.9%)

Counts

4 → 60

Calls

4 calls:

448.0ms	(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))
351.0ms	(cbrt.f64 (cos.f64 y))
12.0ms	(.f64 (.f64 x (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
6.0ms	(*.f64 (cos.f64 y) (cos.f64 y))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 78

Calls

4 calls:

11.0ms	(.f64 (.f64 x (cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
8.0ms	(*.f64 (cos.f64 y) (cos.f64 y))
4.0ms	(cbrt.f64 (*.f64 (cos.f64 y) (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify208.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-neg_binary64`
428×	`*-commutative_binary64`
292×	`cancel-sign-sub-inv_binary64`
279×	`exp-prod_binary64`
277×	`log-prod_binary64`

Counts

138 → 140

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	149	1520
1	339	1327
2	1238	1245
3	2552	1073
4	4266	1057
5	4654	1055
6	4842	1055
7	4906	1055

prune278.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	140	10	150

Error

0.0b

Counts

150 → 10

Alt Table

Status	Error	Program
	25.8b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))
	31.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	32.5b	(.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	29.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
✓	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	27.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))))
▶	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	32.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 3309 to 1104 computations (66.6% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	7.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series2.3s (19.8%)

Counts

3 → 72

Calls

3 calls:

1.5s

(*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))

759.0ms

(cbrt.f64 (*.f64 z (sin.f64 y)))

38.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))

rewrite32.0ms (0.3%)

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:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))

8.0ms

(*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))

3.0ms

(cbrt.f64 (*.f64 z (sin.f64 y)))

simplify220.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
445×	`cancel-sign-sub-inv_binary64`
352×	`*-commutative_binary64`
346×	`fma-def_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

151 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2495
1	410	2016
2	1169	1679
3	2733	1438
4	4659	1438
5	4981	1438
6	4891	1438

prune624.0ms (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	293	4	297
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	297	10	307

Error

0.0b

Counts

307 → 10

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	25.8b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))
	31.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 z (sin.f64 y)))))
✓	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (cbrt.f64 (.f64 x (cos.f64 y)))) (cbrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	10.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 -1) 2) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 y) (/.f64 -1 z)) 2))) (cbrt.f64 (.f64 z (sin.f64 y)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
	32.4b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 8371 to 2068 computations (75.3% saved)

regimes1.2s (10.4%)

Accuracy

Total 0.1b remaining (58.8%)

Threshold costs 0.1b (58.8%)

Counts

136 → 1

Compiler

Compiled 10088 to 6304 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	23	30
2	31	30
3	35	30
4	36	30
5	36	30

end300.0ms (2.5%)

Compiler: Compiled 252 to 150 computations (40.5% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Details

analyze3.0ms (0%)

sample4.6s (39.2%)

simplify33.0ms (0.3%)

prune3.0ms (0%)

localize28.0ms (0.2%)

series60.0ms (0.5%)

rewrite25.0ms (0.2%)

simplify146.0ms (1.2%)

prune183.0ms (1.5%)

localize32.0ms (0.3%)

series40.0ms (0.3%)

rewrite41.0ms (0.3%)

simplify169.0ms (1.4%)

prune303.0ms (2.6%)

localize25.0ms (0.2%)

series818.0ms (6.9%)

rewrite29.0ms (0.2%)

simplify208.0ms (1.8%)

prune278.0ms (2.3%)

localize38.0ms (0.3%)

series2.3s (19.8%)

rewrite32.0ms (0.3%)

simplify220.0ms (1.9%)

prune624.0ms (5.3%)

regimes1.2s (10.4%)

simplify6.0ms (0.1%)

end300.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14