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)

sample240.0ms (2.5%)

Algorithm

1×

intervals

Results

168.0ms	130×	body	2048	valid
25.0ms	60×	body	1024	valid
9.0ms	8×	body	4096	valid
5.0ms	256×	pre	128	true
5.0ms	30×	body	512	valid
2.0ms	18×	body	256	valid
1.0ms	10×	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

59.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	3.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series27.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(/.f64 1 (tan.f64 x))
11.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite55.0ms (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:

18.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
3.0ms	(/.f64 1 (tan.f64 x))

simplify252.0ms (2.6%)

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

prune197.0ms (2%)

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)

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)

series11.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

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

rewrite22.0ms (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:

7.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
5.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(*.f64 1/3 x)

simplify99.0ms (1%)

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

prune122.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	9	122

Error

0.1b

Counts

122 → 9

Alt Table

Status	Error	Program
	30.7b	(+.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))))
	38.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))))
	30.3b	(+.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)))))
	30.2b	(+.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)))))
	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	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 1/3 x)))
	30.2b	(+.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))))
	0.7b	(+.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))))

Compiler

Compiled 2879 to 2303 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

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

simplify64.0ms (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 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	280
1	32	257
2	72	257
3	234	257
4	1075	257
5	4912	257
6	4995	257
7	4968	257

prune81.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Error

0.1b

Counts

86 → 9

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.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)))))
	30.7b	(+.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))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x)))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 1/3 x)))
	38.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3))))
	30.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 x)) (.f64 (sqrt.f64 1/3) (sqrt.f64 x)))))
▶	0.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (*.f64 x (sqrt.f64 1/3)))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))

Compiler

Compiled 1838 to 1465 computations (20.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))))
	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.4b	(*.f64 x (sqrt.f64 1/3))
✓	0.4b	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))

series19.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

8.0ms	(fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))))
8.0ms	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))
3.0ms	(*.f64 x (sqrt.f64 1/3))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

6.0ms	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))
4.0ms	(*.f64 x (sqrt.f64 1/3))
0.0ms	(fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-def_binary64`
401×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
356×	`*-commutative_binary64`
341×	`associate-l_binary64`

Counts

93 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	993
1	145	749
2	364	749
3	899	740
4	1600	740
5	3840	740
6	4831	740
7	4951	740

prune120.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	118	12	130

Error

0.0b

Counts

130 → 12

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.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)))))
	30.7b	(+.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))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.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)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 1/3))))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 1/3 x)))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (sqrt.f64 1/3))))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))
	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 1/3))))))
	30.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/3))) (sqrt.f64 (*.f64 x (sqrt.f64 1/3)))))))
	38.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (sqrt.f64 1/3) (sqrt.f64 1/3)) (sqrt.f64 1/3)))))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/45 (pow.f64 x 3) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 1/3))) (cbrt.f64 (.f64 x (sqrt.f64 1/3)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/3)))))))

Compiler

Compiled 3049 to 2537 computations (16.8% saved)

regimes165.0ms (1.7%)

Accuracy

Total 0.3b remaining (82.7%)

Threshold costs 0.3b (82.7%)

Counts

78 → 1

Compiler

Compiled 3264 to 2716 computations (16.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	24	22
2	23	22

end1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample8.2s (83.3%)

Algorithm

1×

intervals

Results

6.2s	4086×	body	2048	valid
838.0ms	1950×	body	1024	valid
183.0ms	997×	body	512	valid
161.0ms	8000×	pre	128	true
135.0ms	221×	body	4096	valid
58.0ms	520×	body	256	valid
14.0ms	226×	body	128	valid

Compiler

Compiled 323 to 260 computations (19.5% 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%)

sample240.0ms (2.5%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series27.0ms (0.3%)

rewrite55.0ms (0.6%)

simplify252.0ms (2.6%)

prune197.0ms (2%)

localize8.0ms (0.1%)

series11.0ms (0.1%)

rewrite22.0ms (0.2%)

simplify99.0ms (1%)

prune122.0ms (1.2%)

localize10.0ms (0.1%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify64.0ms (0.6%)

prune81.0ms (0.8%)

localize10.0ms (0.1%)

series19.0ms (0.2%)

rewrite12.0ms (0.1%)

simplify85.0ms (0.9%)

prune120.0ms (1.2%)

regimes165.0ms (1.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample8.2s (83.3%)

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