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)

sample9.2s (85%)

Results

7.2s	4110×	body	2048	valid
1.3s	2134×	body	1024	valid
343.0ms	1020×	body	512	valid
195.0ms	215×	body	4096	valid
122.0ms	509×	body	256	valid
39.0ms	268×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% 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

59.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.7b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	2.7b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series24.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(/.f64 1 (tan.f64 x))
10.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite54.0ms (0.5%)

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:

17.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
2.0ms	(/.f64 1 (tan.f64 x))

simplify239.0ms (2.2%)

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

prune192.0ms (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 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))

Compiler

Compiled 10348 to 6497 computations (37.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

5.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
3.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(*.f64 1/45 (pow.f64 x 3))
1.0ms	(*.f64 1/3 x)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
16×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 94

Calls

4 calls:

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

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary64`
481×	`unswap-sqr_binary64`
431×	`*-commutative_binary64`
235×	`fma-def_binary64`
234×	`sqr-pow_binary64`

Counts

103 → 120

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	152	1094
1	318	1020
2	850	1004
3	1878	1004
4	3929	968
5	4727	965
6	4861	965

prune120.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	9	121

Error

0.1b

Counts

121 → 9

Alt Table

Status	Error	Program
	39.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))))
	27.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (.f64 (.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
	35.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (exp.f64 (log.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))))
	32.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 1/45 (pow.f64 x 3)) (.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))
▶	0.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
	32.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))

Compiler

Compiled 2863 to 2290 computations (20% saved)

localize14.0ms (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))
✓	0.3b	(*.f64 (sqrt.f64 1/3) x)
✓	0.3b	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))

series11.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
3.0ms	(*.f64 (sqrt.f64 1/3) x)

rewrite15.0ms (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:

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

simplify72.0ms (0.7%)

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

prune142.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	129	10	139

Error

0.0b

Counts

139 → 10

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	39.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (*.f64 x x) x)))))
▶	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	32.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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))))))
	27.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (.f64 (.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
	32.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 1/45 (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 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
	32.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))

Compiler

Compiled 3600 to 3008 computations (16.4% saved)

localize13.0ms (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))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))
✓	0.3b	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) x)))

series11.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
15×	`associate-l_binary64`
12×	`sqrt-prod_binary64`

Counts

2 → 52

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) x)))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1052×	`fma-def_binary64`
581×	`unswap-sqr_binary64`
359×	`times-frac_binary64`
328×	`*-commutative_binary64`
284×	`sqr-pow_binary64`

Counts

76 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	771
1	160	550
2	493	550
3	720	543
4	1043	528
5	1963	528
6	3517	528
7	4654	528
8	4886	528
9	4994	528

prune152.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	6	2	8
Picked	0	1	1
Done	0	1	1
Total	149	6	155

Error

0.0b

Counts

155 → 6

Alt Table

Status	Error	Program
	1.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 x (pow.f64 (pow.f64 (sqrt.f64 1/3) 1/4) 3))))))
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))))))
✓	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	27.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (.f64 (.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))

Compiler

Compiled 4351 to 3784 computations (13% saved)

regimes164.0ms (1.5%)

Accuracy

Total 0.3b remaining (87.9%)

Threshold costs 0.3b (87.9%)

Counts

82 → 1

Compiler

Compiled 3648 to 3082 computations (15.5% 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	13	20
1	16	20
2	16	20

end134.0ms (1.2%)

Compiler: Compiled 182 to 154 computations (15.4% 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

analyze6.0ms (0.1%)

sample9.2s (85%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series24.0ms (0.2%)

rewrite54.0ms (0.5%)

simplify239.0ms (2.2%)

prune192.0ms (1.8%)

localize8.0ms (0.1%)

series13.0ms (0.1%)

rewrite18.0ms (0.2%)

simplify88.0ms (0.8%)

prune120.0ms (1.1%)

localize14.0ms (0.1%)

series11.0ms (0.1%)

rewrite15.0ms (0.1%)

simplify72.0ms (0.7%)

prune142.0ms (1.3%)

localize13.0ms (0.1%)

series11.0ms (0.1%)

rewrite22.0ms (0.2%)

simplify104.0ms (1%)

prune152.0ms (1.4%)

regimes164.0ms (1.5%)

simplify2.0ms (0%)

end134.0ms (1.2%)

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