Details

analyze5.0ms (0%)

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)

sample9.1s (82.4%)

Results

7.0s	4135×	body	2048	valid
1.4s	2061×	body	1024	valid
355.0ms	1078×	body	512	valid
196.0ms	227×	body	4096	valid
111.0ms	513×	body	256	valid
31.0ms	242×	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

prune5.0ms (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

60.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

279×	`times-frac_binary64`
230×	`add-sqr-sqrt_binary64`
222×	`*-un-lft-identity_binary64`
206×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

1 → 239

Calls

1 calls:

19.0ms

(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify216.0ms (2%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-def_binary64`
387×	`fma-neg_binary64`
371×	`unsub-neg_binary64`
338×	`distribute-rgt-in_binary64`
285×	`associate-l_binary64`

Counts

251 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	8557
1	324	4800
2	803	3343
3	2437	3343
4	4169	3343
5	4866	3343
6	4805	3343

prune179.0ms (1.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	1	252

Error

0.3b

Counts

252 → 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 9671 to 6065 computations (37.3% saved)

localize12.0ms (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 2/945 (pow.f64 x 5))
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(*.f64 1/3 x)

series12.0ms (0.1%)

Counts

4 → 0

Calls

4 calls:

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

rewrite20.0ms (0.2%)

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 1/4725 (pow.f64 x 7))
5.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(*.f64 1/3 x)

simplify79.0ms (0.7%)

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

prune168.0ms (1.5%)

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
✓	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))))
	30.6b	(+.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 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x))))))
	39.3b	(+.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))))))
	30.6b	(+.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 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)))))
▶	0.7b	(+.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)))))
	39.2b	(+.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))))))
	1.6b	(+.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 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))))

Compiler

Compiled 4051 to 3282 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

simplify74.0ms (0.7%)

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

prune184.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	134	12	146

Error

0.1b

Counts

146 → 12

Alt Table

Status	Error	Program
▶	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))))))
	39.3b	(+.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))))
	30.6b	(+.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 (.f64 1/3 x)) (sqrt.f64 (.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))))))
	30.7b	(+.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 (.f64 (sqrt.f64 1/3) x)) (sqrt.f64 (*.f64 (sqrt.f64 1/3) x)))))))
	39.3b	(+.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 (.f64 (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 1/3)) (sqrt.f64 1/3)) (.f64 (*.f64 x x) 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)))))))
	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))))))
	30.6b	(+.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 1/3 (sqrt.f64 x)) (sqrt.f64 x)))))
	39.2b	(+.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))))))
	1.6b	(+.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 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))))

Compiler

Compiled 4869 to 4084 computations (16.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series24.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(*.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:

7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))

simplify69.0ms (0.6%)

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

prune227.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	7	3	10
Picked	1	0	1
Done	0	1	1
Total	169	7	176

Error

Counts

176 → 7

Alt Table

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

Compiler

Compiled 5699 to 4869 computations (14.6% saved)

regimes329.0ms (3%)

Accuracy

Total 0.3b remaining (96%)

Threshold costs 0.3b (96%)

Counts

136 → 1

Compiler

Compiled 8056 to 6872 computations (14.7% saved)

simplify2.0ms (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

end189.0ms (1.7%)

Compiler: Compiled 277 to 237 computations (14.4% 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%)

sample9.1s (82.4%)

simplify11.0ms (0.1%)

prune5.0ms (0%)

localize5.0ms (0%)

series11.0ms (0.1%)

rewrite56.0ms (0.5%)

simplify216.0ms (2%)

prune179.0ms (1.6%)

localize12.0ms (0.1%)

series12.0ms (0.1%)

rewrite20.0ms (0.2%)

simplify79.0ms (0.7%)

prune168.0ms (1.5%)

localize16.0ms (0.1%)

series11.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify74.0ms (0.7%)

prune184.0ms (1.7%)

localize18.0ms (0.2%)

series24.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify69.0ms (0.6%)

prune227.0ms (2.1%)

regimes329.0ms (3%)

simplify2.0ms (0%)

end189.0ms (1.7%)

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