Details

analyze98.0ms (1.4%)

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample81.0ms (1.1%)

Algorithm

1×

intervals

Results

34.0ms	113×	body	1024	valid
16.0ms	57×	body	512	valid
15.0ms	32×	body	2048	valid
2.0ms	38×	body	128	valid
2.0ms	16×	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

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

36.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.6b	(sin.f64 (+.f64 x eps))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

20.3b

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)

series142.0ms (2%)

Error

14.0b

Counts

2 → 22

Calls

2 calls:

80.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
40.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 616 to 371 computations (39.8% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4896	675
1	4896	675

prune48.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Error

0.2b

Counts

49 → 5

Compiler

Compiled 636 to 211 computations (66.8% saved)

localize12.0ms (0.2%)

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)))
0.1b	(*.f64 (sin.f64 eps) (cos.f64 x))
0.2b	(*.f64 (cos.f64 eps) (sin.f64 x))
2.8b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite89.0ms (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 (cos.f64 eps) (sin.f64 x))
5.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))

Compiler

Compiled 1495 to 285 computations (80.9% saved)

series538.0ms (7.5%)

Error

0.2b

Counts

4 → 41

Calls

4 calls:

174.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
145.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
108.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
84.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1682 to 919 computations (45.4% saved)

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5052	1808

prune97.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Error

0.1b

Counts

112 → 10

Compiler

Compiled 2155 to 623 computations (71.1% saved)

localize11.0ms (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 (cos.f64 x) (sin.f64 eps))
0.2b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.3b	(+.f64 (cos.f64 eps) -1)

rewrite89.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-r/_binary64_2066` `-commutative_binary64_2055` `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)))
5.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1405 to 554 computations (60.6% saved)

series435.0ms (6.1%)

Error

0.1b

Counts

4 → 34

Calls

4 calls:

190.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
101.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
99.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
19.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1470 to 952 computations (35.2% saved)

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4936	1571
1	4936	1571

prune102.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Error

0.0b

Counts

112 → 12

Compiler

Compiled 2056 to 880 computations (57.2% saved)

localize15.0ms (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)))
0.3b	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
0.3b	(+.f64 (cos.f64 eps) 1)

rewrite133.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

11.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
9.0ms	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
6.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
4.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 2664 to 872 computations (67.3% saved)

series369.0ms (5.1%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

238.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
64.0ms	(/.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)))
12.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 1123 to 757 computations (32.6% saved)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4980	1531
1	4980	1531

prune108.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Compiler

Compiled 2519 to 1048 computations (58.4% saved)

regimes464.0ms (6.5%)

Accuracy

Total 0.2b remaining (77%)

Threshold costs 0.2b (77%)

Compiler

Compiled 5021 to 3217 computations (35.9% 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

end0.0ms (0%)

sample4.0s (55.4%)

Algorithm

1×

intervals

Results

1.1s	3503×	body	1024	valid
653.0ms	1237×	body	2048	valid
275.0ms	1352×	body	512	valid
88.0ms	1289×	body	128	valid
81.0ms	614×	body	256	valid
5.0ms	5×	body	4096	valid

Compiler

Compiled 1687 to 1088 computations (35.5% saved)

Details

analyze98.0ms (1.4%)

sample81.0ms (1.1%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite41.0ms (0.6%)

series142.0ms (2%)

simplify74.0ms (1%)

prune48.0ms (0.7%)

localize12.0ms (0.2%)

rewrite89.0ms (1.2%)

series538.0ms (7.5%)

simplify75.0ms (1%)

prune97.0ms (1.3%)

localize11.0ms (0.2%)

rewrite89.0ms (1.2%)

series435.0ms (6.1%)

simplify94.0ms (1.3%)

prune102.0ms (1.4%)

localize15.0ms (0.2%)

rewrite133.0ms (1.8%)

series369.0ms (5.1%)

simplify69.0ms (1%)

prune108.0ms (1.5%)

regimes464.0ms (6.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.0s (55.4%)

Profiling