Details

analyze1.8s (14.8%)

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%	100%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.2s (74.5%)

Results

5.4s	2147×	body	2048	valid
2.6s	3069×	body	1024	valid
672.0ms	1519×	body	512	valid
203.0ms	759×	body	256	valid
146.0ms	109×	body	4096	valid
110.0ms	653×	body	128	valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify88.0ms (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

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(/.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)))
✓	1.4b	(-.f64 x (tan.f64 x))
✓	1.4b	(-.f64 x (sin.f64 x))

series22.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

13.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
3.0ms	(-.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:

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))

simplify109.0ms (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

prune73.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	4	153

Error

Counts

153 → 4

Alt Table

Status	Error	Program
	33.2b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	43.7b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
▶	30.1b	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
	30.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))

Compiler

Compiled 3188 to 915 computations (71.3% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
	1.4b	(-.f64 x (tan.f64 x))
✓	1.4b	(+.f64 x (neg.f64 (sin.f64 x)))

series12.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
3.0ms	(+.f64 x (neg.f64 (sin.f64 x)))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out_binary64`

Counts

2 → 76

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
4.0ms	(+.f64 x (neg.f64 (sin.f64 x)))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
511×	`fma-neg_binary64`
410×	`fma-def_binary64`
322×	`distribute-rgt-in_binary64`
267×	`distribute-lft-in_binary64`

Counts

100 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2057
1	417	1972
2	1308	1943
3	4516	1931
4	4976	1931
5	4926	1931

prune88.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Alt Table

Status	Error	Program
	33.2b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	43.7b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	30.1b	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
▶	30.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))

Compiler

Compiled 3292 to 894 computations (72.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (cos.f64 x))
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
✓	2.0b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

series65.0ms (0.5%)

Counts

4 → 32

Calls

4 calls:

47.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
8.0ms	(/.f64 1 (cos.f64 x))
7.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
3.0ms	(/.f64 (sin.f64 x) x)

rewrite30.0ms (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:

12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
6.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
3.0ms	(/.f64 (sin.f64 x) x)
2.0ms	(/.f64 1 (cos.f64 x))

simplify99.0ms (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

prune144.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	215	4	219

Error

Counts

219 → 4

Alt Table

Status	Error	Program
▶	33.2b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	43.7b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	30.1b	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	30.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))

Compiler

Compiled 4490 to 2455 computations (45.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.2b	(.f64 9/40 (.f64 x x))
✓	13.5b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series10.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
2.0ms	(.f64 9/40 (.f64 x x))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
4.0ms	(.f64 9/40 (.f64 x x))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-neg_binary64`
399×	`associate-+r+_binary64`
379×	`associate-+l+_binary64`
320×	`fma-def_binary64`
300×	`times-frac_binary64`

Counts

88 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1147
1	199	1072
2	668	980
3	2038	980
4	4543	969
5	4942	969

prune52.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	33.2b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	43.7b	(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	30.1b	(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
✓	30.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))

Compiler

Compiled 1565 to 1142 computations (27% saved)

regimes77.0ms (0.6%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Counts

27 → 3

Compiler

Compiled 696 to 452 computations (35.1% saved)

bsearch49.0ms (0.4%)

Steps

Iters	Range		Point
10	3.916820032061989e-9	72095225371.52528	2.6632315197980545
7	-0.5146009897314334	-0.0049087755324097255	-0.03232663999321673

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	67
1	39	67
2	51	67
3	57	67
4	60	67
5	59	67

end129.0ms (1%)

Compiler: Compiled 147 to 91 computations (38.1% saved)

Details

analyze1.8s (14.8%)

sample9.2s (74.5%)

simplify88.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series22.0ms (0.2%)

rewrite22.0ms (0.2%)

simplify109.0ms (0.9%)

prune73.0ms (0.6%)

localize14.0ms (0.1%)

series12.0ms (0.1%)

rewrite18.0ms (0.1%)

simplify112.0ms (0.9%)

prune88.0ms (0.7%)

localize9.0ms (0.1%)

series65.0ms (0.5%)

rewrite30.0ms (0.2%)

simplify99.0ms (0.8%)

prune144.0ms (1.2%)

localize7.0ms (0.1%)

series10.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify71.0ms (0.6%)

prune52.0ms (0.4%)

regimes77.0ms (0.6%)

bsearch49.0ms (0.4%)

simplify4.0ms (0%)

end129.0ms (1%)

Profiling