Details

analyze2.6s (19.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample199.0ms (1.5%)

Algorithm

1×

intervals

Results

48.0ms	60×	body	1024	valid
22.0ms	131×	body	128	valid
22.0ms	41×	body	512	valid
8.0ms	24×	body	256	valid
2.0ms	12×	body	128	invalid
1.0ms	6×	body	128	nan

Compiler

Compiled 64 to 50 computations (21.9% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

640×	`distribute-rgt-neg-in_binary64`
474×	`fma-neg_binary64`
418×	`distribute-lft-neg-in_binary64`
379×	`div-sub_binary64`
378×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	35
1	49	28
2	100	28
3	195	28
4	391	28
5	1075	28
6	2543	28
7	4200	28
8	4955	28

prune5.0ms (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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.5b	(+.f64 (neg.f64 (.f64 x (/.f64 1 (tan.f64 B)))) (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (neg.f64 (/.f64 1 2)))))
▶	14.4b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))

Status

Error

Program

14.5b

(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) 2) (*.f64 2 x)) (neg.f64 (/.f64 1 2)))))

▶

14.4b

(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 153 to 108 computations (29.4% saved)

localize51.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 x (tan.f64 B))
✓	0.2b	(/.f64 F (sin.f64 B))
✓	6.9b	(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
✓	17.6b	(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series297.0ms (2.3%)

Counts

4 → 80

Calls

4 calls:

143.0ms	(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
95.0ms	(/.f64 x (tan.f64 B))
43.0ms	(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
16.0ms	(/.f64 F (sin.f64 B))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 123

Calls

4 calls:

7.0ms	(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
7.0ms	(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
3.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 F (sin.f64 B))

simplify167.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

302×	`fma-def_binary64`
223×	`*-commutative_binary64`
221×	`associate-r_binary64`
218×	`fma-neg_binary64`
202×	`+-commutative_binary64`

Counts

203 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	500	5883
1	1360	5603
2	4518	5575
3	4984	5575
4	4932	5575

prune361.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	262	9	271
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	264	9	273

Error

0.0b

Counts

273 → 9

Alt Table

Status	Error	Program
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
	30.3b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	15.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
▶	10.3b	(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.0b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	28.9b	(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.5b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 10223 to 5708 computations (44.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 x (tan.f64 B))
✓	0.3b	(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
✓	0.5b	(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
	17.6b	(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series222.0ms (1.7%)

Counts

2 → 44

Calls

2 calls:

148.0ms	(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
73.0ms	(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
4.0ms	(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

simplify131.0ms (1%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
258×	`sub-neg_binary64`
210×	`fma-neg_binary64`
171×	`associate-r_binary64`

Counts

96 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3456
1	819	3211
2	2879	3191
3	4806	3191
4	4973	3191
5	4942	3191

prune367.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	270	9	279

Error

0.0b

Counts

279 → 9

Alt Table

Status	Error	Program
▶	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
	30.3b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	15.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
✓	10.3b	(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.0b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	28.9b	(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.5b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 10496 to 6372 computations (39.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 F (sin.f64 B))
✓	0.6b	(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
✓	6.9b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))
✓	18.1b	(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

series280.0ms (2.2%)

Counts

3 → 68

Calls

3 calls:

181.0ms

(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))

54.0ms

(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))

45.0ms

(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
35×	`add-sqr-sqrt_binary64`
21×	`unpow-prod-down_binary64`
20×	`associate-l_binary64`

Counts

3 → 125

Calls

3 calls:

9.0ms

(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))

6.0ms

(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))

1.0ms

(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-r_binary64`
376×	`fma-def_binary64`
287×	`fma-neg_binary64`
243×	`associate-l_binary64`
190×	`associate--l+_binary64`

Counts

193 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	560	7303
1	1574	6751
2	4896	6751
3	5091	6751

prune551.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	374	1	375
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	375	9	384

Error

0.0b

Counts

384 → 9

Alt Table

Status	Error	Program
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (.f64 (.f64 (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4) (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4)) (.f64 (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4) (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4)))) (/.f64 x (tan.f64 B)))
	33.5b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))
▶	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	15.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
✓	10.3b	(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.0b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	28.9b	(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	30.3b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 18705 to 11619 computations (37.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 F (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
	6.9b	(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
	17.6b	(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series23.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

23.0ms

(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

5.0ms

(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-def_binary64`
518×	`times-frac_binary64`
405×	`distribute-rgt-neg-in_binary64`
331×	`cancel-sign-sub-inv_binary64`
276×	`distribute-lft-neg-in_binary64`

Counts

58 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	840
1	219	766
2	574	759
3	1741	757
4	3804	757
5	4613	757
6	4996	757
7	4924	757

prune339.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	292	9	301

Error

0.0b

Counts

301 → 9

Alt Table

Status	Error	Program
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (.f64 (.f64 (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4) (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4)) (.f64 (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4) (pow.f64 (sqrt.f64 (fma.f64 2 x (fma.f64 F F 2))) -1/4)))) (/.f64 x (tan.f64 B)))
	33.5b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))
✓	14.4b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	15.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
✓	10.3b	(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
	33.0b	(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	28.9b	(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	30.3b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 11511 to 5824 computations (49.4% saved)

regimes2.2s (16.9%)

Accuracy

Total 0.3b remaining (83.6%)

Threshold costs 0.3b (83.6%)

Counts

272 → 3

Compiler

Compiled 33580 to 22168 computations (34% saved)

bsearch197.0ms (1.5%)

Steps

Iters	Range		Point
10	1321.0914523920765	5478899448720051.0	44861197.49111579
9	-3.453433677548891e+49	-3.8026514137939516e+43	-2.133618383434366e+44

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	70
1	35	70
2	42	70
3	46	70
4	49	70
5	50	70
6	49	70

end1.0ms (0%)

Compiler: Compiled 49 to 28 computations (42.9% saved)

sample4.5s (35%)

Algorithm

1×

intervals

Results

1.7s	2155×	body	1024	valid
750.0ms	4185×	body	128	valid
559.0ms	1076×	body	512	valid
209.0ms	577×	body	256	valid
111.0ms	662×	body	128	invalid
17.0ms	114×	body	128	nan
10.0ms	7×	body	2048	valid

Compiler

Compiled 310 to 208 computations (32.9% saved)

Details

analyze2.6s (19.9%)

sample199.0ms (1.5%)

simplify52.0ms (0.4%)

prune5.0ms (0%)

localize51.0ms (0.4%)

series297.0ms (2.3%)

rewrite27.0ms (0.2%)

simplify167.0ms (1.3%)

prune361.0ms (2.8%)

localize20.0ms (0.2%)

series222.0ms (1.7%)

rewrite11.0ms (0.1%)

simplify131.0ms (1%)

prune367.0ms (2.8%)

localize17.0ms (0.1%)

series280.0ms (2.2%)

rewrite31.0ms (0.2%)

simplify164.0ms (1.3%)

prune551.0ms (4.3%)

localize17.0ms (0.1%)

series23.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify100.0ms (0.8%)

prune339.0ms (2.6%)

regimes2.2s (16.9%)

bsearch197.0ms (1.5%)

simplify4.0ms (0%)

end1.0ms (0%)

sample4.5s (35%)

Profiling