Details

analyze1.8s (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.2s (72.7%)

Results

5.4s	2130×	body	2048	valid
2.2s	3095×	body	1024	valid
603.0ms	1481×	body	512	valid
391.0ms	109×	body	4096	valid
328.0ms	802×	body	256	valid
107.0ms	639×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

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

28.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.5b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.1b	(-.f64 x (sin.f64 x))
✓	1.2b	(-.f64 x (tan.f64 x))

series19.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune93.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	4	154

Error

0.0b

Counts

154 → 4

Alt Table

Status	Error	Program
	34.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
	54.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))
▶	28.5b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	28.7b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

Compiler

Compiled 3219 to 909 computations (71.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.0b	(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
	1.1b	(-.f64 x (sin.f64 x))
	1.2b	(-.f64 x (tan.f64 x))

series38.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

38.0ms

(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`exp-prod_binary64`
25×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`

Counts

1 → 42

Calls

1 calls:

14.0ms

(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
718×	`associate-/l*_binary64`
607×	`associate-/r*_binary64`
232×	`associate-*l/_binary64`
231×	`associate-*r/_binary64`

Counts

54 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	1562
1	378	1509
2	1330	1349
3	4911	1329
4	5488	1329

prune678.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	206	4	210

Error

0.0b

Counts

210 → 4

Alt Table

Status	Error	Program
	34.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
	54.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))
✓	28.5b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	28.7b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

Compiler

Compiled 4869 to 1674 computations (65.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	1.1b	(-.f64 x (sin.f64 x))
	1.2b	(-.f64 x (tan.f64 x))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 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 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
415×	`unswap-sqr_binary64`
339×	`times-frac_binary64`
226×	`associate-/l*_binary64`
200×	`sub-neg_binary64`

Counts

23 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	646
1	169	617
2	542	583
3	2706	567
4	4880	567
5	5049	567

prune82.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Error

0.0b

Counts

189 → 4

Alt Table

Status	Error	Program
▶	34.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
	54.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))
✓	28.5b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	28.7b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

Compiler

Compiled 4111 to 1365 computations (66.8% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 9/40 (*.f64 x x) -1/2)

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 9/40 (*.f64 x x) -1/2)

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 9/40 (*.f64 x x) -1/2)

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5149	197

prune8.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	16	4	20

Error

0.0b

Counts

20 → 4

Alt Table

Status	Error	Program
✓	34.3b	(fma.f64 9/40 (*.f64 x x) -1/2)
	54.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (cbrt.f64 (-.f64 x (sin.f64 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))
✓	28.5b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	28.7b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

Compiler

Compiled 211 to 127 computations (39.8% saved)

regimes70.0ms (0.6%)

Accuracy

Total 0.0b remaining (6.4%)

Threshold costs 0.0b (6.4%)

Counts

26 → 3

Compiler

Compiled 688 to 444 computations (35.5% saved)

bsearch53.0ms (0.4%)

Steps

Iters	Range		Point
10	5.775946466907837e-16	7.73402573904606	0.005389730405536012
9	-21.124866710609645	-0.00017212100510171632	-0.004877358576892519

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	24	52
2	32	52
3	36	52
4	38	52
5	38	52

end83.0ms (0.7%)

Compiler: Compiled 133 to 70 computations (47.4% saved)

Details

analyze1.8s (14.5%)

sample9.2s (72.7%)

simplify87.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series19.0ms (0.1%)

rewrite22.0ms (0.2%)

simplify102.0ms (0.8%)

prune93.0ms (0.7%)

localize20.0ms (0.2%)

series38.0ms (0.3%)

rewrite26.0ms (0.2%)

simplify92.0ms (0.7%)

prune678.0ms (5.4%)

localize9.0ms (0.1%)

series9.0ms (0.1%)

rewrite1.0ms (0%)

simplify59.0ms (0.5%)

prune82.0ms (0.7%)

localize3.0ms (0%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify49.0ms (0.4%)

prune8.0ms (0.1%)

regimes70.0ms (0.6%)

bsearch53.0ms (0.4%)

simplify3.0ms (0%)

end83.0ms (0.7%)

Profiling