Details

analyze2.5s (22.2%)

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)

sample196.0ms (1.7%)

Algorithm

1×

intervals

Results

116.0ms	62×	body	2048	valid
42.0ms	95×	body	1024	valid
11.0ms	46×	body	512	valid
7.0ms	7×	body	4096	valid
4.0ms	25×	body	256	valid
2.0ms	21×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify89.0ms (0.8%)

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

31.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.6b	(/.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.5b	(-.f64 x (tan.f64 x))
✓	1.5b	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

8.0ms	(/.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))
1.0ms	(sin.f64 x)

series26.0ms (0.2%)

Counts

4 → 34

Calls

4 calls:

11.0ms	(-.f64 x (tan.f64 x))
10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
1.0ms	(sin.f64 x)

simplify155.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
313×	`cancel-sign-sub-inv_binary64`
252×	`associate-/l/_binary64`
221×	`associate-/r/_binary64`
204×	`distribute-rgt-in_binary64`

Counts

157 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	3109
1	618	2685
2	2075	2567
3	4500	2563
4	4985	2563
5	4872	2563

prune96.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	3	232

Error

0.0b

Counts

232 → 3

Alt Table

Status	Error	Program
▶	31.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	32.2b	(+.f64 (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (pow.f64 x 3)))) (-.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 3) (.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
	31.5b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 3511 to 1059 computations (69.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 27/112000 (pow.f64 x 6))
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	0.3b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	19.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
0.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))

series64.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

22.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
21.0ms	(*.f64 27/112000 (pow.f64 x 6))
14.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
6.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

445×	`fma-neg_binary64`
370×	`fma-def_binary64`
341×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
292×	`exp-prod_binary64`

Counts

115 → 193

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2086
1	260	1929
2	799	1728
3	2810	1715
4	4377	1706
5	4997	1706
6	4754	1706

prune103.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	193	3	196

Error

Counts

196 → 3

Alt Table

Status	Error	Program
▶	31.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (.f64 27/112000 (pow.f64 x 6)))) 1/2)
	32.2b	(+.f64 (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (pow.f64 x 3)))) (-.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 3) (.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
	31.5b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 3560 to 2647 computations (25.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (.f64 27/112000 (pow.f64 x 6)))) 1/2)
	0.0b	(*.f64 27/112000 (pow.f64 x 6))
✓	0.1b	(fma.f64 9/40 (.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (.f64 27/112000 (pow.f64 x 6))))
✓	19.3b	(fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6)))

rewrite7.0ms (0.1%)

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:

3.0ms

(-.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6)))) 1/2)

0.0ms

(fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6)))

0.0ms

(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6))))

series41.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

21.0ms

(fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6)))

13.0ms

(fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6))))

7.0ms

(-.f64 (fma.f64 9/40 (*.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (*.f64 27/112000 (pow.f64 x 6)))) 1/2)

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
473×	`associate-+l+_binary64`
441×	`associate-+r+_binary64`
356×	`exp-prod_binary64`
333×	`*-commutative_binary64`

Counts

87 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1835
1	185	1711
2	348	1640
3	1415	1624
4	3443	1624
5	4878	1624
6	4763	1624

prune140.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	203	3	206

Error

Counts

206 → 3

Alt Table

Status	Error	Program
✓	31.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (.f64 27/112000 (pow.f64 x 6)))) 1/2)
	32.2b	(+.f64 (+.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (pow.f64 x 3)))) (-.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) 3) (.f64 (pow.f64 x 3) (pow.f64 (cos.f64 x) 2))))))
▶	31.5b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 3760 to 2798 computations (25.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 x)
✓	0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
	1.5b	(-.f64 x (tan.f64 x))
	1.5b	(-.f64 x (sin.f64 x))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 150

Calls

1 calls:

10.0ms

(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

series10.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

simplify168.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

519×	`times-frac_binary64`
337×	`associate-/l*_binary64`
274×	`associate-r_binary64`
274×	`associate-/r*_binary64`
262×	`associate-l_binary64`

Counts

162 → 312

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	4916
1	420	4509
2	1295	4375
3	4444	4362
4	4966	4362

prune166.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	446	1	447
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	447	3	450

Error

Counts

450 → 3

Alt Table

Status	Error	Program
	31.6b	(/.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (/.f64 1 (-.f64 x (sin.f64 x))))
✓	31.5b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
✓	31.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (fma.f64 (pow.f64 x 4) -27/2800 (.f64 27/112000 (pow.f64 x 6)))) 1/2)

Compiler

Compiled 6450 to 1938 computations (70% saved)

regimes218.0ms (1.9%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Compiler

Compiled 3025 to 1805 computations (40.3% saved)

bsearch47.0ms (0.4%)

Steps

Iters	Range		Point
8	0.0007180392414806993	1.7475808034814253	0.09629485008899653
9	-335542.28695022623	-0.02730429450461721	-2.594104887854674

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
14×	`*-commutative_binary64`
13×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	157
1	75	157
2	90	157
3	108	157
4	126	157
5	136	157
6	141	157
7	142	157
8	140	157

end2.0ms (0%)

Compiler: Compiled 103 to 62 computations (39.8% saved)

sample7.1s (61.5%)

Algorithm

1×

intervals

Results

4.5s	2026×	body	2048	valid
1.5s	2991×	body	1024	valid
406.0ms	1523×	body	512	valid
121.0ms	110×	body	4096	valid
117.0ms	706×	body	256	valid
65.0ms	644×	body	128	valid

Compiler

Compiled 159 to 102 computations (35.8% saved)

Iter	Nodes	Cost
0	54	157
1	75	157
2	90	157
3	108	157
4	126	157
5	136	157
6	141	157
7	142	157
8	140	157

Iter	Nodes	Cost
0	54	157
1	75	157
2	90	157
3	108	157
4	126	157
5	136	157
6	141	157
7	142	157
8	140	157

Details

analyze2.5s (22.2%)

sample196.0ms (1.7%)

simplify89.0ms (0.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite22.0ms (0.2%)

series26.0ms (0.2%)

simplify155.0ms (1.3%)

prune96.0ms (0.8%)

localize12.0ms (0.1%)

rewrite12.0ms (0.1%)

series64.0ms (0.6%)

simplify128.0ms (1.1%)

prune103.0ms (0.9%)

localize10.0ms (0.1%)

rewrite7.0ms (0.1%)

series41.0ms (0.4%)

simplify108.0ms (0.9%)

prune140.0ms (1.2%)

localize8.0ms (0.1%)

rewrite28.0ms (0.2%)

series10.0ms (0.1%)

simplify168.0ms (1.5%)

prune166.0ms (1.4%)

regimes218.0ms (1.9%)

bsearch47.0ms (0.4%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample7.1s (61.5%)

Profiling

Iter	Nodes	Cost
0	54	157
1	75	157
2	90	157
3	108	157
4	126	157
5	136	157
6	141	157
7	142	157
8	140	157