Details

analyze100.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

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

Symmetry

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample76.0ms (1%)

Algorithm

1×

intervals

Results

35.0ms	113×	body	1024	valid
17.0ms	36×	body	2048	valid
8.0ms	43×	body	512	valid
3.0ms	45×	body	128	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	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

39.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.7b	(sin.f64 (+.f64 x eps))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

20.8b

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`add-cube-cbrt_binary64_2159` `cancel-sign-sub-inv_binary64_2090`
2×	`sin-sum_binary64_2257` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`diff-sin_binary64_2274` `diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `associate--l+_binary64_2061`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series147.0ms (1.9%)

Error

15.6b

Counts

2 → 23

Calls

2 calls:

78.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
41.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 647 to 389 computations (39.9% saved)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4922	713
1	4922	713

prune51.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

0.3b

Counts

50 → 4

Compiler

Compiled 656 to 227 computations (65.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
0.2b	(*.f64 (cos.f64 eps) (sin.f64 x))
0.2b	(*.f64 (sin.f64 eps) (cos.f64 x))
1.4b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite97.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_2146`
11×	`add-log-exp_binary64_2163` `*-un-lft-identity_binary64_2124`
9×	`add-cube-cbrt_binary64_2159`
8×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-l_binary64_2065` `associate-r_binary64_2064`
3×	`cancel-sign-sub-inv_binary64_2090`
2×	`sum-log_binary64_2215` `diff-log_binary64_2216` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`
1×	`flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `associate--l+_binary64_2061` `sin-cos-mult_binary64_2280` `flip3-+_binary64_2127` `flip-+_binary64_2098` `+-commutative_binary64_2054`

Counts

4 → 66

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
5.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
5.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1495 to 285 computations (80.9% saved)

series552.0ms (7%)

Error

0.2b

Counts

4 → 42

Calls

4 calls:

183.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
137.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
111.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
94.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1713 to 937 computations (45.3% saved)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5171	1846

prune103.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Error

0.1b

Counts

112 → 12

Compiler

Compiled 2235 to 668 computations (70.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.2b	(*.f64 (cos.f64 x) (sin.f64 eps))
1.7b	(+.f64 (cos.f64 eps) -1)

rewrite94.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64_2146`
12×	`*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `associate-r_binary64_2064`
6×	`associate-l_binary64_2065`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`sum-log_binary64_2215` `difference-of-sqr--1_binary64_2095` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `-commutative_binary64_2055` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-r/_binary64_2066` `associate-+r+_binary64_2056`

Counts

4 → 68

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
5.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
4.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1405 to 554 computations (60.6% saved)

series423.0ms (5.3%)

Error

0.1b

Counts

4 → 33

Calls

4 calls:

175.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
107.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
97.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
18.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1399 to 905 computations (35.3% saved)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5396	1545

prune102.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Error

0.1b

Counts

113 → 10

Compiler

Compiled 1979 to 836 computations (57.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
0.2b	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
0.2b	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
0.5b	(+.f64 (cos.f64 eps) 1)

rewrite137.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

21×	`*-un-lft-identity_binary64_2124`
20×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-r_binary64_2064`
17×	`add-sqr-sqrt_binary64_2146`
13×	`add-cube-cbrt_binary64_2159`
8×	`pow1_binary64_2185` `times-frac_binary64_2130`
6×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-l_binary64_2065`
4×	`distribute-lft-out_binary64_2075` `distribute-rgt-neg-out_binary64_2084` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-rgt-neg-in_binary64_2082` `distribute-lft-neg-in_binary64_2081`
2×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `distribute-frac-neg_binary64_2087` `div-inv_binary64_2121`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `neg-mul-1_binary64_2120` `associate-r/_binary64_2066` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/l_binary64_2069`

Counts

4 → 95

Calls

4 calls:

12.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
9.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
9.0ms	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
4.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 2664 to 872 computations (67.3% saved)

series383.0ms (4.9%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

239.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
73.0ms	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
38.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
16.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 1175 to 788 computations (32.9% saved)

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4893	1541
1	4893	1541

prune109.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Error

0.1b

Counts

125 → 9

Compiler

Compiled 2542 to 1055 computations (58.5% saved)

regimes630.0ms (8%)

Accuracy

Total 0.2b remaining (78.6%)

Threshold costs 0.2b (78.6%)

Compiler

Compiled 6689 to 4301 computations (35.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

Removed

()

end0.0ms (0%)

sample4.5s (56.6%)

Algorithm

1×

intervals

Results

1.0s	3452×	body	1024	valid
611.0ms	1219×	body	2048	valid
288.0ms	1459×	body	512	valid
85.0ms	587×	body	256	valid
82.0ms	1281×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 2246 to 1452 computations (35.4% saved)

Details

analyze100.0ms (1.3%)

sample76.0ms (1%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite41.0ms (0.5%)

series147.0ms (1.9%)

simplify75.0ms (0.9%)

prune51.0ms (0.6%)

localize11.0ms (0.1%)

rewrite97.0ms (1.2%)

series552.0ms (7%)

simplify80.0ms (1%)

prune103.0ms (1.3%)

localize13.0ms (0.2%)

rewrite94.0ms (1.2%)

series423.0ms (5.3%)

simplify78.0ms (1%)

prune102.0ms (1.3%)

localize14.0ms (0.2%)

rewrite137.0ms (1.7%)

series383.0ms (4.9%)

simplify87.0ms (1.1%)

prune109.0ms (1.4%)

regimes630.0ms (8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.5s (56.6%)

Profiling