Details

analyze1.9s (16.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample8.2s (68.3%)

Results

5.0s	2107×	body	2048	valid
2.0s	3068×	body	1024	valid
623.0ms	1523×	body	512	valid
213.0ms	778×	body	256	valid
168.0ms	123×	body	4096	valid
105.0ms	657×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess69.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`fma-def_binary64`
421×	`div-sub_binary64`
332×	`times-frac_binary64`
157×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	75	14
5	130	14
6	260	14
7	543	14
8	1322	14
9	2479	14
10	3294	14
11	3659	14
12	3788	14
13	3815	14
14	3825	14
15	3829	14
16	3829	14
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 6 computations (40% saved)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`fma-def_binary64`
421×	`div-sub_binary64`
332×	`times-frac_binary64`
157×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	75	14
5	130	14
6	260	14
7	543	14
8	1322	14
9	2479	14
10	3294	14
11	3659	14
12	3788	14
13	3815	14
14	3825	14
15	3829	14
16	3829	14

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.7b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 39 to 21 computations (46.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.4b	(-.f64 x (tan.f64 x))
✓	1.5b	(-.f64 x (sin.f64 x))

series16.0ms (0.1%)

Counts

3 → 30

Calls

9 calls:

3.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))	x	-inf
3.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))	x	inf
2.0ms	(-.f64 x (tan.f64 x))	x	inf
2.0ms	(-.f64 x (tan.f64 x))	x	-inf
1.0ms	(-.f64 x (sin.f64 x))	x	0

rewrite149.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`prod-diff_binary64`
336×	`egg-rr`
170×	`log1p-udef_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	26
1	170	26
2	2750	26

Stop Event

1×	node limit

Counts

3 → 336

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
295×	`fma-def_binary64`
275×	`sub-neg_binary64`
219×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	658
1	261	654
2	860	614
3	4331	602

Stop Event

1×	node limit

Counts

366 → 367

prune241.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	363	4	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	364	4	368

Error

0.0b

Counts

368 → 4

Alt Table

Status	Error	Program
▶	30.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	49.9b	(+.f64 (fma.f64 x (/.f64 1 (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x)))) (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1))))
	31.1b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
	32.5b	(+.f64 -1/2 (fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800)))

Compiler

Compiled 16771 to 4235 computations (74.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
✓	0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
	1.4b	(-.f64 x (tan.f64 x))
✓	1.5b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

series22.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

4.0ms	(/.f64 x (-.f64 x (tan.f64 x)))	x	inf
4.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))	x	inf
4.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))	x	-inf
3.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))	x	-inf
2.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))	x	inf

rewrite89.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`fma-def_binary64`
288×	`fma-neg_binary64`
227×	`egg-rr`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
1	198	34
2	3395	34

Stop Event

1×	node limit

Counts

3 → 227

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-neg_binary64`
428×	`times-frac_binary64`
259×	`associate-/l*_binary64`
243×	`sub-neg_binary64`
204×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1068
1	226	1064
2	746	1024
3	4039	990

Stop Event

1×	node limit

Counts

263 → 268

prune196.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	393	1	394
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	394	4	398

Error

0.0b

Counts

398 → 4

Alt Table

Status	Error	Program
✓	30.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	32.5b	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))
	49.9b	(+.f64 (fma.f64 x (/.f64 1 (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x)))) (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1))))
▶	31.1b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 10160 to 2636 computations (74.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.1b	(*.f64 (cos.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

series22.0ms (0.2%)

Counts

4 → 18

Calls

12 calls:

4.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))	x	-inf
4.0ms	(/.f64 (sin.f64 x) x)	x	0
3.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))	x	inf
2.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))	x	-inf
2.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))	x	inf

rewrite88.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`fma-def_binary64`
278×	`fma-neg_binary64`
257×	`egg-rr`
208×	`log1p-udef_binary64`
207×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	227	35
2	3474	35

Stop Event

1×	node limit

Counts

4 → 257

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

437×	`distribute-rgt-neg-in_binary64`
434×	`cancel-sign-sub-inv_binary64`
268×	`unswap-sqr_binary64`
251×	`*-commutative_binary64`
247×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	210
1	159	202
2	426	190
3	1473	190
4	3641	190

Stop Event

1×	node limit

Counts

275 → 283

prune189.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	283	4	287

Error

0.0b

Counts

287 → 4

Alt Table

Status	Error	Program
✓	30.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
▶	32.5b	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))
	49.9b	(+.f64 (fma.f64 x (/.f64 1 (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x)))) (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1))))
✓	31.1b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 6377 to 2436 computations (61.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 4) -27/2800 -1/2)
✓	17.3b	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

series6.0ms (0%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))	x	-inf
1.0ms	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))	x	inf
1.0ms	(fma.f64 (pow.f64 x 4) -27/2800 -1/2)	x	inf
1.0ms	(fma.f64 (pow.f64 x 4) -27/2800 -1/2)	x	-inf
1.0ms	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))	x	0

rewrite41.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log1p-expm1-u_binary64`
769×	`expm1-log1p-u_binary64`
160×	`log1p-udef_binary64`
92×	`add-sqr-sqrt_binary64`
91×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	208	23
2	2148	23

Stop Event

1×	node limit

Counts

2 → 47

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-neg_binary64`
590×	`distribute-rgt-neg-in_binary64`
407×	`fma-def_binary64`
361×	`cancel-sign-sub-inv_binary64`
251×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	262
1	47	258
2	100	228
3	277	228
4	980	228
5	2585	228
6	4283	228

Stop Event

1×	node limit

Counts

71 → 58

prune32.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	58	4	62

Error

0.0b

Counts

62 → 4

Alt Table

Status	Error	Program
✓	30.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	32.5b	(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))
	49.9b	(+.f64 (fma.f64 x (/.f64 1 (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x)))) (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (-.f64 x (tan.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) 1))))
✓	31.1b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))

Compiler

Compiled 981 to 678 computations (30.9% saved)

regimes296.0ms (2.5%)

Accuracy

Total 0.2b remaining (87.9%)

Threshold costs 0.2b (87.9%)

Counts

115 → 3

Compiler

Compiled 3638 to 2326 computations (36.1% saved)

bsearch58.0ms (0.5%)

Algorithm

2×	binary-search

Calls

2 calls:

31.0ms	x
23.0ms	x

Steps

Iters	Point		Range
0.02855440944818922	∈ [	0.00040233536306803205	,	0.15862257151393017	]
-2.646218411575844	∈ [	-96032410410.23123	,	-0.0033161191515068515	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	67
1	36	67
2	44	67
3	50	67
4	54	67
5	55	67

Stop Event

1×

saturated

end87.0ms (0.7%)

Stop Event

1×

fuel

Compiler

Compiled 188 to 100 computations (46.8% saved)

Details

analyze1.9s (16.1%)

sample8.2s (68.3%)

preprocess69.0ms (0.6%)

simplify62.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series16.0ms (0.1%)

rewrite149.0ms (1.3%)

simplify53.0ms (0.4%)

prune241.0ms (2%)

localize8.0ms (0.1%)

series22.0ms (0.2%)

rewrite89.0ms (0.7%)

simplify48.0ms (0.4%)

prune196.0ms (1.6%)

localize9.0ms (0.1%)

series22.0ms (0.2%)

rewrite88.0ms (0.7%)

simplify33.0ms (0.3%)

prune189.0ms (1.6%)

localize6.0ms (0.1%)

series6.0ms (0%)

rewrite41.0ms (0.3%)

simplify33.0ms (0.3%)

prune32.0ms (0.3%)

regimes296.0ms (2.5%)

bsearch58.0ms (0.5%)

simplify4.0ms (0%)

end87.0ms (0.7%)

Profiling