Details

analyze5.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 16 to 12 computations (25% saved)

sample12.3s (80.1%)

Results

10.0s	4204×	body	2048	valid
1.5s	2036×	body	1024	valid
383.0ms	1037×	body	512	valid
243.0ms	223×	body	4096	valid
125.0ms	515×	body	256	valid
35.0ms	241×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% saved)

simplify11.0ms (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

59.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.8b	(-.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)))

series31.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(/.f64 1 (tan.f64 x))
12.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite53.0ms (0.3%)

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:

15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
3.0ms	(/.f64 1 (tan.f64 x))

simplify255.0ms (1.7%)

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

prune277.0ms (1.8%)

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 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))

Compiler

Compiled 10360 to 6507 computations (37.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/4725 (pow.f64 x 7))
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.3b	(*.f64 1/3 x)

series12.0ms (0.1%)

Counts

4 → 0

Calls

4 calls:

4.0ms	(*.f64 1/4725 (pow.f64 x 7))
3.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(*.f64 1/45 (pow.f64 x 3))
2.0ms	(*.f64 1/3 x)

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
29×	`associate-r_binary64`
21×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

5.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(*.f64 1/3 x)
4.0ms	(*.f64 1/4725 (pow.f64 x 7))
4.0ms	(*.f64 2/945 (pow.f64 x 5))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
544×	`unswap-sqr_binary64`
387×	`*-commutative_binary64`
328×	`log-prod_binary64`
309×	`associate-/l*_binary64`

Counts

107 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	179	1082
1	330	1006
2	780	993
3	1238	993
4	2384	939
5	4485	939
6	4911	939

prune167.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Error

0.2b

Counts

138 → 8

Alt Table

Status	Error	Program
	35.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x)))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))
▶	0.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (*.f64 (sqrt.f64 1/3) x)))))
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 x)) (.f64 (sqrt.f64 1/3) (sqrt.f64 x))))))
	41.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))
	41.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 x) (.f64 1/3 x)) (.f64 1/3 x))))))

Compiler

Compiled 4055 to 3284 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.3b	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
✓	0.4b	(*.f64 (sqrt.f64 1/3) x)

series13.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

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

rewrite12.0ms (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:

6.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
4.0ms	(*.f64 (sqrt.f64 1/3) x)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
332×	`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

prune224.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	135	11	146

Error

0.1b

Counts

146 → 11

Alt Table

Status	Error	Program
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 x)) (.f64 (sqrt.f64 1/3) (sqrt.f64 x))))))
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))
	41.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 x) (.f64 1/3 x)) (.f64 1/3 x))))))
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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)))))))
	41.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) x) 3))))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))
▶	0.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 x)) (sqrt.f64 x))))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))))
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 x)))))))

Compiler

Compiled 4811 to 4030 computations (16.2% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.2b	(.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))

series43.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

30.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
13.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))

rewrite29.0ms (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:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
9.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

simplify127.0ms (0.8%)

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

prune484.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	7	2	9
Picked	1	0	1
Done	0	1	1
Total	169	6	175

Error

Counts

175 → 6

Alt Table

Status	Error	Program
	41.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (sqrt.f64 1/3) 3/2) x) 3))))))
	0.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 x)) (sqrt.f64 x))))))
	0.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.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))))))

Compiler

Compiled 5651 to 4827 computations (14.6% saved)

regimes745.0ms (4.8%)

Accuracy

Total 0.3b remaining (94.6%)

Threshold costs 0.3b (94.6%)

Counts

133 → 1

Compiler

Compiled 7856 to 6690 computations (14.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	26	31
2	26	31

end303.0ms (2%)

Compiler: Compiled 229 to 195 computations (14.8% 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

analyze5.0ms (0%)

sample12.3s (80.1%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

series31.0ms (0.2%)

rewrite53.0ms (0.3%)

simplify255.0ms (1.7%)

prune277.0ms (1.8%)

localize17.0ms (0.1%)

series12.0ms (0.1%)

rewrite21.0ms (0.1%)

simplify97.0ms (0.6%)

prune167.0ms (1.1%)

localize16.0ms (0.1%)

series13.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify81.0ms (0.5%)

prune224.0ms (1.5%)

localize39.0ms (0.3%)

series43.0ms (0.3%)

rewrite29.0ms (0.2%)

simplify127.0ms (0.8%)

prune484.0ms (3.1%)

regimes745.0ms (4.8%)

simplify3.0ms (0%)

end303.0ms (2%)

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