Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample345.0ms (3.7%)

Algorithm

1×

intervals

Results

265.0ms	121×	body	2048	valid
35.0ms	77×	body	1024	valid
6.0ms	33×	body	512	valid
5.0ms	256×	pre	128	true
4.0ms	16×	body	256	valid
2.0ms	4×	body	4096	valid
0.0ms	5×	body	128	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

prune2.0ms (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

60.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	2.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series26.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(/.f64 1 (tan.f64 x))
10.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
215×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

2 → 273

Calls

2 calls:

14.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
3.0ms	(/.f64 1 (tan.f64 x))

simplify256.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
466×	`fma-def_binary64`
354×	`distribute-rgt-in_binary64`
331×	`cancel-sign-sub-inv_binary64`
277×	`associate-l_binary64`

Counts

297 → 302

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	8645
1	364	6130
2	911	4575
3	2803	4281
4	4238	4246
5	4940	4246
6	4768	4246

prune187.0ms (2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	1	303

Error

0.3b

Counts

303 → 1

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))

Compiler

Compiled 10336 to 6487 computations (37.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(*.f64 1/3 x)

series4.0ms (0%)

Counts

2 → 0

Calls

2 calls:

3.0ms	(*.f64 1/45 (pow.f64 x 3))
2.0ms	(*.f64 1/3 x)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

5.0ms	(*.f64 1/45 (pow.f64 x 3))
3.0ms	(*.f64 1/3 x)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-l_binary64`
574×	`associate-r_binary64`
469×	`fma-def_binary64`
366×	`log-prod_binary64`
326×	`cube-prod_binary64`

Counts

53 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	496
1	156	444
2	392	443
3	2007	443
4	3157	411
5	4364	411
6	4951	411
7	4911	411

prune59.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Error

0.2b

Counts

71 → 8

Alt Table

Status	Error	Program
	32.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
	32.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x)))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
▶	0.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (*.f64 (sqrt.f64 1/3) x)))
	39.2b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 x x) x))))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))
	39.2b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)))

Compiler

Compiled 1213 to 952 computations (21.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.4b	(*.f64 (sqrt.f64 1/3) x)
✓	0.4b	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))

series11.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
3.0ms	(*.f64 (sqrt.f64 1/3) x)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
4.0ms	(*.f64 (sqrt.f64 1/3) x)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
342×	`associate-l_binary64`
332×	`unswap-sqr_binary64`
263×	`associate-*r/_binary64`
234×	`associate-*l/_binary64`

Counts

59 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	459
1	121	420
2	338	419
3	628	411
4	824	411
5	1265	411
6	3215	411
7	4671	411
8	4933	411

prune110.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	101	12	113

Error

0.1b

Counts

113 → 12

Alt Table

Status	Error	Program
	32.8b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) x)) (sqrt.f64 (*.f64 (sqrt.f64 1/3) x)))))
	32.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x)))
	1.6b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) x)) (cbrt.f64 (.f64 (sqrt.f64 1/3) x))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) x)))))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
	32.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
▶	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 1/3) x))))
	39.2b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))))
	0.9b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (.f64 (sqrt.f64 (cbrt.f64 1/3)) (*.f64 (sqrt.f64 1/3) x))))

Compiler

Compiled 2291 to 1930 computations (15.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
✓	0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

series23.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
8.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`associate-l_binary64`
11×	`associate-r_binary64`

Counts

2 → 58

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
4.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-/r/_binary64`
560×	`associate-/l/_binary64`
541×	`fma-def_binary64`
480×	`*-commutative_binary64`
276×	`sqr-pow_binary64`

Counts

82 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	95	1147
1	190	997
2	602	971
3	873	779
4	1358	728
5	2345	713
6	4971	713

prune143.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	7	3	10
Picked	1	0	1
Done	0	1	1
Total	136	7	143

Error

Counts

143 → 7

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))
	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/4)) (pow.f64 (sqrt.f64 (sqrt.f64 1/3)) 3/2))))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))))
	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 1/3) x))))
	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))))

Compiler

Compiled 2914 to 2526 computations (13.3% saved)

regimes192.0ms (2.1%)

Accuracy

Total 0.3b remaining (83.7%)

Threshold costs 0.3b (83.7%)

Counts

97 → 1

Compiler

Compiled 3648 to 3150 computations (13.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	12	13

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample7.6s (81.5%)

Algorithm

1×

intervals

Results

5.7s	3996×	body	2048	valid
829.0ms	2023×	body	1024	valid
209.0ms	1039×	body	512	valid
157.0ms	8000×	pre	128	true
123.0ms	212×	body	4096	valid
54.0ms	496×	body	256	valid
14.0ms	234×	body	128	valid

Compiler

Compiled 168 to 146 computations (13.1% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Details

analyze6.0ms (0.1%)

sample345.0ms (3.7%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

series26.0ms (0.3%)

rewrite51.0ms (0.6%)

simplify256.0ms (2.8%)

prune187.0ms (2%)

localize5.0ms (0.1%)

series4.0ms (0%)

rewrite9.0ms (0.1%)

simplify88.0ms (0.9%)

prune59.0ms (0.6%)

localize9.0ms (0.1%)

series11.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify73.0ms (0.8%)

prune110.0ms (1.2%)

localize10.0ms (0.1%)

series23.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify66.0ms (0.7%)

prune143.0ms (1.5%)

regimes192.0ms (2.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.6s (81.5%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12