Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.6%	50.4%	0
49.6%	0%	50.4%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.2s (81.8%)

Results

2.9s	4381×	body	2048	valid
830.0ms	2147×	body	1024	valid
270.0ms	972×	body	512	valid
100.0ms	529×	body	256	valid
27.0ms	227×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
4×	`+-commutative_binary64`
3×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	13	6
3	19	6
4	26	6
5	36	6
6	44	6
7	53	6
8	56	6
9	39	6

prune1.0ms (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

31.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.8b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 15 to 12 computations (20% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(-.f64 1 (cos.f64 x))

series2.0ms (0%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(-.f64 1 (cos.f64 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

4.0ms

(-.f64 1 (cos.f64 x))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
792×	`fma-def_binary64`
476×	`unsub-neg_binary64`
319×	`cancel-sign-sub-inv_binary64`
265×	`*-commutative_binary64`

Counts

35 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	434
1	152	378
2	411	331
3	1316	331
4	3243	331
5	4306	331
6	4860	331
7	4996	331
8	4792	331

prune33.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	2	44

Error

0.0b

Counts

44 → 2

Alt Table

Status	Error	Program
	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
▶	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))

Compiler

Compiled 699 to 368 computations (47.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
✓	0.0b	(*.f64 1/2 (pow.f64 x 2))
✓	0.0b	(*.f64 1/720 (pow.f64 x 6))
✓	0.1b	(*.f64 1/24 (pow.f64 x 4))

series13.0ms (0.3%)

Counts

4 → 6

Calls

4 calls:

5.0ms	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
3.0ms	(*.f64 1/720 (pow.f64 x 6))
3.0ms	(*.f64 1/24 (pow.f64 x 4))
2.0ms	(*.f64 1/2 (pow.f64 x 2))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
19×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

6.0ms	(*.f64 1/2 (pow.f64 x 2))
6.0ms	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2))) (*.f64 1/24 (pow.f64 x 4)))
4.0ms	(*.f64 1/24 (pow.f64 x 4))
4.0ms	(*.f64 1/720 (pow.f64 x 6))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-+l+_binary64`
320×	`fma-def_binary64`
304×	`*-commutative_binary64`
182×	`cancel-sign-sub-inv_binary64`
164×	`distribute-rgt-in_binary64`

Counts

111 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	1732
1	361	1385
2	927	1318
3	2377	1305
4	4858	1305

prune140.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	156	2	158

Error

Counts

158 → 2

Alt Table

Status	Error	Program
	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
▶	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 (.f64 1/2 x) x)) (.f64 1/24 (pow.f64 x 4)))

Compiler

Compiled 3767 to 3040 computations (19.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 (.f64 1/2 x) x)) (.f64 1/24 (pow.f64 x 4)))
	0.0b	(*.f64 1/720 (pow.f64 x 6))
	0.1b	(*.f64 1/24 (pow.f64 x 4))

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 (*.f64 1/2 x) x)) (*.f64 1/24 (pow.f64 x 4)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
3×	`fma-neg_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 22

Calls

1 calls:

6.0ms

(-.f64 (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 (*.f64 1/2 x) x)) (*.f64 1/24 (pow.f64 x 4)))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

439×	`fma-neg_binary64`
412×	`associate-l_binary64`
381×	`associate-r_binary64`
372×	`cancel-sign-sub-inv_binary64`
290×	`fma-def_binary64`

Counts

34 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	876
1	158	748
2	521	712
3	2834	698
4	4619	698
5	4832	698

prune95.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	114	2	116

Error

Counts

116 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
✓	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 (.f64 1/2 x) x)) (.f64 1/24 (pow.f64 x 4)))

Compiler

Compiled 2800 to 2157 computations (23% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
	0.0b	(*.f64 1/720 (pow.f64 x 6))
✓	0.1b	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))

series9.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))
4.0ms	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))
0.0ms	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

407×	`distribute-lft-in_binary64`
407×	`distribute-rgt-in_binary64`
371×	`fma-neg_binary64`
314×	`fma-def_binary64`
305×	`unswap-sqr_binary64`

Counts

44 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	854
1	74	746
2	153	746
3	636	746
4	2344	746
5	4864	746
6	5030	746

prune69.0ms (1.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	79	2	81

Error

Counts

81 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
✓	0.0b	(-.f64 (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 (.f64 1/2 x) x)) (.f64 1/24 (pow.f64 x 4)))

Compiler

Compiled 1675 to 1201 computations (28.3% saved)

regimes108.0ms (2.1%)

Accuracy

Total 0.0b remaining (18.2%)

Threshold costs 0.0b (18.2%)

Counts

44 → 1

Compiler

Compiled 1813 to 1415 computations (22% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	26	25
2	34	25
3	38	25
4	41	25
5	42	25
6	41	25

end65.0ms (1.3%)

Compiler: Compiled 70 to 54 computations (22.9% saved)

Details

analyze1.0ms (0%)

sample4.2s (81.8%)

simplify7.0ms (0.1%)

prune1.0ms (0%)

localize2.0ms (0%)

series2.0ms (0%)

rewrite5.0ms (0.1%)

simplify95.0ms (1.9%)

prune33.0ms (0.7%)

localize9.0ms (0.2%)

series13.0ms (0.3%)

rewrite23.0ms (0.5%)

simplify68.0ms (1.3%)

prune140.0ms (2.7%)

localize11.0ms (0.2%)

series5.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify69.0ms (1.3%)

prune95.0ms (1.9%)

localize17.0ms (0.3%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (1.4%)

prune69.0ms (1.4%)

regimes108.0ms (2.1%)

simplify2.0ms (0%)

end65.0ms (1.3%)

Profiling