Details

analyze6.0ms (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)

sample9.7s (82.3%)

Results

7.2s	4176×	body	2048	valid
1.8s	2081×	body	1024	valid
342.0ms	1035×	body	512	valid
212.0ms	243×	body	4096	valid
113.0ms	484×	body	256	valid
36.0ms	237×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% saved)

simplify13.0ms (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

59.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.4b	(-.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))
✓	3.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series30.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(/.f64 1 (tan.f64 x))
12.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite60.0ms (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:

16.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

simplify258.0ms (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

prune191.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	2	303

Error

0.3b

Counts

303 → 2

Alt Table

Status	Error	Program
	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 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 10376 to 6519 computations (37.2% saved)

localize9.0ms (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:

4.0ms	(*.f64 1/3 x)
3.0ms	(+.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))

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:

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

simplify95.0ms (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

prune138.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Error

0.1b

Counts

122 → 8

Alt Table

Status	Error	Program
	30.2b	(+.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))))
	34.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	40.4b	(+.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)))))
	1.5b	(+.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)))))
▶	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
	34.0b	(+.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))))
	34.0b	(+.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 2849 to 2275 computations (20.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

730×	`distribute-rgt-in_binary64`
716×	`distribute-lft-in_binary64`
306×	`distribute-lft-out_binary64`
284×	`distribute-rgt-out_binary64`
274×	`associate-l_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	277
1	32	254
2	72	254
3	234	254
4	1075	254
5	4912	254
6	4995	254
7	4968	254

prune58.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	53	8	61

Error

0.1b

Counts

61 → 8

Alt Table

Status	Error	Program
	30.2b	(+.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))))
	34.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	40.4b	(+.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)))))
▶	1.5b	(+.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)))))
✓	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
	34.0b	(+.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))))
	34.0b	(+.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 1310 to 1021 computations (22.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))
	0.3b	(*.f64 1/3 x)
✓	0.5b	(.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
✓	0.7b	(cbrt.f64 (*.f64 1/3 x))

series110.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

46.0ms	(.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
42.0ms	(cbrt.f64 (*.f64 1/3 x))
23.0ms	(.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))
4.0ms	(.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
2.0ms	(cbrt.f64 (*.f64 1/3 x))

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
489×	`*-commutative_binary64`
469×	`associate-r_binary64`
415×	`sqr-pow_binary64`
368×	`unswap-sqr_binary64`

Counts

115 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	1128
1	149	1049
2	420	985
3	1173	924
4	2297	830
5	3346	830
6	4439	830
7	4846	830

prune214.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	203	11	214

Error

0.1b

Counts

214 → 11

Alt Table

Status	Error	Program
	2.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) 8) (cbrt.f64 (cbrt.f64 (*.f64 1/3 x))))))
	2.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x)))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))))) (cbrt.f64 (*.f64 1/3 x)))))
	30.2b	(+.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))))
	34.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	2.0b	(+.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))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) 2) (cbrt.f64 (cbrt.f64 (*.f64 1/3 x)))))))
	40.4b	(+.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)))))
	2.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (cbrt.f64 (.f64 1/3 x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x)))) (cbrt.f64 (*.f64 1/3 x)))))
✓	0.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
	34.0b	(+.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))))
	34.0b	(+.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 6344 to 5141 computations (19% saved)

regimes415.0ms (3.5%)

Accuracy

Total 0.2b remaining (65.9%)

Threshold costs 0.2b (65.9%)

Counts

167 → 1

Compiler

Compiled 8468 to 6946 computations (18% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	21	27
2	21	27

end243.0ms (2.1%)

Compiler: Compiled 343 to 277 computations (19.2% 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%)

sample9.7s (82.3%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

series30.0ms (0.3%)

rewrite60.0ms (0.5%)

simplify258.0ms (2.2%)

prune191.0ms (1.6%)

localize9.0ms (0.1%)

series13.0ms (0.1%)

rewrite18.0ms (0.2%)

simplify95.0ms (0.8%)

prune138.0ms (1.2%)

localize8.0ms (0.1%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify70.0ms (0.6%)

prune58.0ms (0.5%)

localize12.0ms (0.1%)

series110.0ms (0.9%)

rewrite16.0ms (0.1%)

simplify99.0ms (0.8%)

prune214.0ms (1.8%)

regimes415.0ms (3.5%)

simplify3.0ms (0%)

end243.0ms (2.1%)

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