Details

analyze1.8s (15%)

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)

sample9.1s (76.1%)

Results

5.6s	2036×	body	2048	valid
2.2s	3145×	body	1024	valid
548.0ms	1501×	body	512	valid
336.0ms	817×	body	256	valid
153.0ms	100×	body	4096	valid
106.0ms	657×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify85.0ms (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

31.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.7b	(/.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)))
✓	1.3b	(-.f64 x (tan.f64 x))
✓	1.4b	(-.f64 x (sin.f64 x))

series21.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
8.0ms	(-.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:

9.0ms	(/.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))

simplify105.0ms (0.9%)

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 → 152

Iterations

Useful iterations: 2 (0.0ms)

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

prune68.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
	31.9b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
▶	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))
✓	31.7b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3148 to 893 computations (71.6% saved)

localize11.0ms (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)))
✓	0.2b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	19.1b	(-.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))

series14.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

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

rewrite13.0ms (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:

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))
4.0ms	(*.f64 27/112000 (pow.f64 x 6))
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)))

simplify120.0ms (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 → 125

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

prune100.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	125	3	128

Error

Counts

128 → 3

Alt Table

Status	Error	Program
▶	31.9b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	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))
✓	31.7b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3427 to 2571 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (cos.f64 x))
✓	0.2b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
✓	1.8b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

series29.0ms (0.2%)

Counts

4 → 32

Calls

4 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
8.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
7.0ms	(/.f64 1 (cos.f64 x))
3.0ms	(/.f64 (sin.f64 x) x)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
41×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 138

Calls

4 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
5.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
2.0ms	(/.f64 (sin.f64 x) x)
2.0ms	(/.f64 1 (cos.f64 x))

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

443×	`fma-def_binary64`
410×	`associate-*l/_binary64`
341×	`associate-/l*_binary64`
334×	`distribute-rgt-in_binary64`
312×	`associate-*r/_binary64`

Counts

170 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2417
1	573	2236
2	1485	2213
3	4391	2213
4	4980	2213

prune119.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	215	3	218

Error

Counts

218 → 3

Alt Table

Status	Error	Program
✓	31.9b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	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))
✓	31.7b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 4443 to 2426 computations (45.4% saved)

regimes74.0ms (0.6%)

Accuracy

Total 0.0b remaining (21.7%)

Threshold costs 0.0b (21.7%)

Counts

23 → 3

Compiler

Compiled 710 to 538 computations (24.2% saved)

bsearch50.0ms (0.4%)

Steps

Iters	Range		Point
10	5.5246575259987277e-14	195002.517381923	0.10015501263761316
8	-128.94964516157012	-0.02919319809264242	-0.08512733689796546

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	26	50
1	33	50
2	41	50
3	45	50
4	47	50
5	47	50

end83.0ms (0.7%)

Compiler: Compiled 112 to 81 computations (27.7% saved)

Details

analyze1.8s (15%)

sample9.1s (76.1%)

simplify85.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.2%)

rewrite22.0ms (0.2%)

simplify105.0ms (0.9%)

prune68.0ms (0.6%)

localize11.0ms (0.1%)

series14.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify120.0ms (1%)

prune100.0ms (0.8%)

localize9.0ms (0.1%)

series29.0ms (0.2%)

rewrite28.0ms (0.2%)

simplify97.0ms (0.8%)

prune119.0ms (1%)

regimes74.0ms (0.6%)

bsearch50.0ms (0.4%)

simplify3.0ms (0%)

end83.0ms (0.7%)

Profiling