Details

analyze24.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample90.0ms (1.7%)

Algorithm

1×

intervals

Results

32.0ms	61×	body	1024	valid
15.0ms	150×	body	128	valid
8.0ms	27×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	18×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	15
2	23	15
3	26	15
4	27	15
5	26	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 47 to 28 computations (40.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 v)
✓	0.0b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (sin.f64 v))

series43.0ms (0.8%)

Counts

3 → 32

Calls

3 calls:

33.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
8.0ms	(*.f64 e (sin.f64 v))
3.0ms	(sin.f64 v)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

4.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))
1.0ms	(sin.f64 v)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
500×	`fma-def_binary64`
460×	`fma-neg_binary64`
310×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`

Counts

84 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1794
1	502	1638
2	1985	1594
3	4907	1594
4	5178	1594

prune96.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	7	97

Error

0.0b

Counts

97 → 7

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (cbrt.f64 (.f64 e (sin.f64 v)))) (cbrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	6.1b	(/.f64 (*.f64 e (cbrt.f64 (pow.f64 (sin.f64 v) 3))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	21.5b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	29.6b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2277 to 1194 computations (47.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 v)
✓	0.0b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
✓	0.2b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))
✓	0.3b	(*.f64 (sqrt.f64 e) (sin.f64 v))

series70.0ms (1.3%)

Counts

3 → 44

Calls

3 calls:

45.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
14.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
10.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 72

Calls

3 calls:

7.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
7.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))
4.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
463×	`fma-neg_binary64`
330×	`cancel-sign-sub-inv_binary64`
321×	`associate-/l/_binary64`
214×	`associate-r_binary64`

Counts

116 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2164
1	588	1939
2	2399	1885
3	4574	1885
4	4955	1885

prune134.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	149	8	157

Error

0.0b

Counts

157 → 8

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.9b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (.f64 (sqrt.f64 e) (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	6.1b	(/.f64 (*.f64 e (cbrt.f64 (pow.f64 (sin.f64 v) 3))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	21.5b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	0.8b	(/.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e))) (.f64 (sqrt.f64 (cbrt.f64 e)) (.f64 (sqrt.f64 e) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
▶	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 3693 to 1630 computations (55.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 e))
✓	0.2b	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))
✓	0.3b	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))

series406.0ms (7.8%)

Counts

4 → 68

Calls

4 calls:

225.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))
151.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
19.0ms	(sqrt.f64 (sqrt.f64 e))
10.0ms	(.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 101

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))
7.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))
7.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
1.0ms	(sqrt.f64 (sqrt.f64 e))

simplify103.0ms (2%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
493×	`*-commutative_binary64`
299×	`fma-def_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

169 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2429
1	371	1885
2	1274	1837
3	2541	1837
4	4681	1837
5	5009	1837

prune160.0ms (3.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	172	8	180

Error

Counts

180 → 8

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e)))))) (fma.f64 e (cos.f64 v) 1))
✓	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.9b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (.f64 (sqrt.f64 e) (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	0.6b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)))) (.f64 (.f64 (sin.f64 v) (pow.f64 (sqrt.f64 (sqrt.f64 e)) 3)) (sqrt.f64 (sqrt.f64 (cbrt.f64 e))))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	21.5b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
✓	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4499 to 1597 computations (64.5% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 e) (.f64 (*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e)))))
✓	0.3b	(*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e))))
✓	0.3b	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e))))
✓	0.6b	(cbrt.f64 e)

series744.0ms (14.4%)

Counts

4 → 80

Calls

4 calls:

424.0ms	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e))))
265.0ms	(.f64 (sqrt.f64 e) (.f64 (*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e)))))
31.0ms	(cbrt.f64 e)
25.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e))))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
27×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 104

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 e) (.f64 (*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e)))))
11.0ms	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e))))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e))))
1.0ms	(cbrt.f64 e)

simplify151.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
540×	`cancel-sign-sub-inv_binary64`
346×	`unswap-sqr_binary64`
338×	`associate-r_binary64`
336×	`associate-l_binary64`

Counts

184 → 183

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	221	3860
1	504	3027
2	1668	2785
3	3020	2542
4	4748	2528
5	4948	2528
6	4965	2528

prune181.0ms (3.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	201	8	209

Error

Counts

209 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 e)))))) (fma.f64 e (cos.f64 v) 1))
✓	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.9b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (.f64 (sqrt.f64 e) (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	0.6b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)))) (.f64 (.f64 (sin.f64 v) (pow.f64 (sqrt.f64 (sqrt.f64 e)) 3)) (sqrt.f64 (sqrt.f64 (cbrt.f64 e))))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	21.5b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
✓	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 6534 to 2496 computations (61.8% saved)

regimes184.0ms (3.5%)

Accuracy

Total 0.1b remaining (76.6%)

Threshold costs 0.1b (76.6%)

Counts

59 → 1

Compiler

Compiled 3701 to 2249 computations (39.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	11	15

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.5s (47.6%)

Algorithm

1×

intervals

Results

1.0s	1950×	body	1024	valid
420.0ms	4538×	body	128	valid
276.0ms	999×	body	512	valid
177.0ms	8000×	pre	128	true
93.0ms	511×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 208 to 130 computations (37.5% saved)

Details

analyze24.0ms (0.5%)

sample90.0ms (1.7%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series43.0ms (0.8%)

rewrite10.0ms (0.2%)

simplify76.0ms (1.5%)

prune96.0ms (1.9%)

localize10.0ms (0.2%)

series70.0ms (1.3%)

rewrite22.0ms (0.4%)

simplify88.0ms (1.7%)

prune134.0ms (2.6%)

localize14.0ms (0.3%)

series406.0ms (7.8%)

rewrite31.0ms (0.6%)

simplify103.0ms (2%)

prune160.0ms (3.1%)

localize20.0ms (0.4%)

series744.0ms (14.4%)

rewrite38.0ms (0.7%)

simplify151.0ms (2.9%)

prune181.0ms (3.5%)

regimes184.0ms (3.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (47.6%)

Profiling