Details

analyze39.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample210.0ms (1.9%)

Algorithm

1×

intervals

Results

86.0ms	110×	body	1024	valid
85.0ms	44×	body	2048	valid
17.0ms	43×	body	512	valid
5.0ms	41×	body	128	valid
5.0ms	18×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify19.0ms (0.2%)

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	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune3.0ms (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

38.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	1.9b	(sin.f64 (+.f64 x eps))

series20.0ms (0.2%)

Counts

3 → 52

Calls

3 calls:

11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	(sin.f64 (+.f64 x eps))
3.0ms	(sin.f64 x)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 51

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))
2.0ms	(sin.f64 x)

simplify149.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1023×	`fma-neg_binary64`
545×	`fma-def_binary64`
414×	`cancel-sign-sub-inv_binary64`
330×	`sub-neg_binary64`
259×	`distribute-rgt-neg-in_binary64`

Counts

103 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1361
1	342	1285
2	1084	1214
3	2734	1207
4	4586	1200
5	4987	1200
6	4830	1200

prune109.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

0.2b

Counts

111 → 4

Alt Table

Status	Error	Program
	27.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
▶	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
	27.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	42.1b	(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) 3) (pow.f64 (sin.f64 x) 3)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (sin.f64 (+.f64 eps x)) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))))

Compiler

Compiled 1940 to 616 computations (68.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (+.f64 eps x))
✓	0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
✓	1.8b	(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

series27.0ms (0.2%)

Counts

3 → 72

Calls

3 calls:

17.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
4.0ms	(+.f64 x (+.f64 eps x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 50

Calls

3 calls:

8.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
5.0ms	(+.f64 x (+.f64 eps x))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
401×	`fma-def_binary64`
390×	`associate-l_binary64`
359×	`associate-r_binary64`
313×	`distribute-rgt-neg-in_binary64`

Counts

122 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2063
1	375	1829
2	1037	1598
3	3117	1591
4	4705	1591
5	4957	1591

prune144.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	8	116
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Error

0.1b

Counts

120 → 10

Alt Table

Status	Error	Program
	38.5b	(.f64 2 (.f64 (sqrt.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
	27.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	36.9b	(.f64 2 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))) (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
	27.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	11.8b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
	29.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 (.f64 1/2 eps)) (.f64 (sin.f64 (*.f64 1/2 eps)) x))))
	28.4b	(.f64 2 (.f64 (*.f64 (sqrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (sin.f64 (/.f64 eps 2))) (sqrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
▶	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
	12.6b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))

Compiler

Compiled 3073 to 2137 computations (30.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
✓	0.3b	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
✓	0.5b	(expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
✓	1.7b	(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))

series45.0ms (0.4%)

Counts

4 → 96

Calls

4 calls:

16.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
16.0ms	(expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
7.0ms	(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))
6.0ms	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
2.0ms	(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))
0.0ms	(expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

simplify151.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

726×	`sub-neg_binary64`
501×	`*-commutative_binary64`
486×	`cancel-sign-sub-inv_binary64`
305×	`associate--r+_binary64`
231×	`associate--l+_binary64`

Counts

147 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2947
1	528	2777
2	1720	2690
3	4161	2690
4	4824	2690
5	5014	2690

prune276.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	114	10	124

Error

0.1b

Counts

124 → 10

Alt Table

Status	Error	Program
	28.4b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (sqrt.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))))
	11.9b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)))))
	27.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	36.9b	(.f64 2 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))) (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
	27.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	11.8b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
	29.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 (.f64 1/2 eps)) (.f64 (sin.f64 (*.f64 1/2 eps)) x))))
✓	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
▶	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
	12.6b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))

Compiler

Compiled 3574 to 2714 computations (24.1% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
✓	0.4b	(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
	1.7b	(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))

series1.1s (9.4%)

Counts

3 → 72

Calls

3 calls:

1.0s

(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))

26.0ms

(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))

10.0ms

(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

9.0ms

(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))

8.0ms

(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))

1.0ms

(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

simplify166.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

928×	`times-frac_binary64`
504×	`fma-def_binary64`
295×	`cancel-sign-sub-inv_binary64`
274×	`fma-neg_binary64`
153×	`neg-mul-1_binary64`

Counts

114 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	2534
1	524	2355
2	1755	2264
3	4735	2246
4	5002	2246

prune313.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Error

0.1b

Counts

145 → 9

Alt Table

Status	Error	Program
	11.9b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)))))
	11.8b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 (fma.f64 x 2 eps))) 1)))))
	27.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	27.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	11.8b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
	29.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 (.f64 1/2 eps)) (.f64 (sin.f64 (*.f64 1/2 eps)) x))))
✓	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
✓	11.6b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
	12.6b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))

Compiler

Compiled 3813 to 2920 computations (23.4% saved)

regimes1.3s (12%)

Accuracy

Total 0.1b remaining (17%)

Threshold costs 0.1b (17%)

Counts

136 → 3

Compiler

Compiled 7413 to 5543 computations (25.2% saved)

bsearch181.0ms (1.6%)

Steps

Iters	Range		Point
10	2.0999388781604722e-18	1.4471309635938159e-8	1.2208837136567138e-8
10	-67351557194.80865	-1.7125811283861844e-7	-1.7466463302217585e-7

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	79
1	37	79
2	43	79
3	45	79
4	46	79
5	46	79

end2.0ms (0%)

Compiler: Compiled 52 to 29 computations (44.2% saved)

sample6.7s (59.7%)

Algorithm

1×

intervals

Results

2.8s	3431×	body	1024	valid
2.1s	1207×	body	2048	valid
785.0ms	1406×	body	512	valid
195.0ms	605×	body	256	valid
195.0ms	1350×	body	128	valid
4.0ms	1×	body	4096	valid

Compiler

Compiled 258 to 185 computations (28.3% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze39.0ms (0.3%)

sample210.0ms (1.9%)

simplify19.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series20.0ms (0.2%)

rewrite23.0ms (0.2%)

simplify149.0ms (1.3%)

prune109.0ms (1%)

localize11.0ms (0.1%)

series27.0ms (0.2%)

rewrite22.0ms (0.2%)

simplify107.0ms (1%)

prune144.0ms (1.3%)

localize15.0ms (0.1%)

series45.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify151.0ms (1.4%)

prune276.0ms (2.5%)

localize31.0ms (0.3%)

series1.1s (9.4%)

rewrite21.0ms (0.2%)

simplify166.0ms (1.5%)

prune313.0ms (2.8%)

regimes1.3s (12%)

bsearch181.0ms (1.6%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample6.7s (59.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11