Details

analyze150.0ms (1.5%)

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)

sample77.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	111×	body	1024	valid
22.0ms	38×	body	2048	valid
10.0ms	52×	body	512	valid
2.0ms	38×	body	128	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

38.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.7b	(sin.f64 (+.f64 x eps))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

22.3b

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`add-cube-cbrt_binary64_1477` `cancel-sign-sub-inv_binary64_1408`
2×	`sin-sum_binary64_1575` `pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
1×	`diff-sin_binary64_1592` `diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379`

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 373 to 99 computations (73.5% saved)

series201.0ms (2%)

Error

13.5b

Counts

2 → 23

Calls

2 calls:

116.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
57.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 600 to 390 computations (35% saved)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5076	717

prune49.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.2b

Counts

50 → 3

Compiler

Compiled 553 to 209 computations (62.2% saved)

localize12.0ms (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)))
0.1b	(*.f64 (sin.f64 eps) (cos.f64 x))
0.1b	(*.f64 (cos.f64 eps) (sin.f64 x))
2.6b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite173.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1464`
11×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
8×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`sum-log_binary64_1533` `diff-log_binary64_1534` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379` `sin-cos-mult_binary64_1598` `flip3-+_binary64_1445` `flip-+_binary64_1416` `+-commutative_binary64_1372`

Counts

4 → 66

Calls

4 calls:

8.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
8.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
5.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))
5.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))

Compiler

Compiled 1415 to 267 computations (81.1% saved)

series902.0ms (8.9%)

Error

0.2b

Counts

4 → 45

Calls

4 calls:

317.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
227.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
166.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))
159.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))

Compiler

Compiled 1709 to 1040 computations (39.1% saved)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5034	1948

prune166.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Error

0.1b

Counts

114 → 11

Compiler

Compiled 1941 to 668 computations (65.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)

rewrite138.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

11×	`*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
8×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477`
4×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`sum-log_binary64_1533` `difference-of-sqr--1_binary64_1413` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372` `cbrt-prod_binary64_1473`
2×	`cbrt-div_binary64_1474`
1×	`pow1/3_binary64_1524`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 2608 to 1096 computations (58% saved)

series1.2s (11.6%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

993.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
40.0ms	(+.f64 (cos.f64 eps) -1)
38.0ms	(+.f64 (cos.f64 eps) -1)
38.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 3831 to 2191 computations (42.8% saved)

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4954	1787
1	4954	1787

prune206.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Error

0.1b

Counts

92 → 13

Compiler

Compiled 4235 to 1925 computations (54.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3)))))
1.4b	(-.f64 (cos.f64 eps) 1)
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)

rewrite167.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`*-un-lft-identity_binary64_1442`
12×	`add-sqr-sqrt_binary64_1464`
10×	`add-log-exp_binary64_1481`
6×	`add-cube-cbrt_binary64_1477`
4×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `cancel-sign-sub-inv_binary64_1408` `cbrt-prod_binary64_1473`
2×	`sum-log_binary64_1533` `difference-of-sqr--1_binary64_1413` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372` `difference-of-squares_binary64_1411` `cbrt-div_binary64_1474`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394` `pow1/3_binary64_1524`

Counts

4 → 57

Calls

4 calls:

5.0ms	(-.f64 (cos.f64 eps) 1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3)))))

Compiler

Compiled 3008 to 1384 computations (54% saved)

series1.2s (11.8%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

1.0s	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3)))))
43.0ms	(+.f64 (cos.f64 eps) -1)
39.0ms	(+.f64 (cos.f64 eps) -1)
39.0ms	(-.f64 (cos.f64 eps) 1)

Compiler

Compiled 3948 to 2308 computations (41.5% saved)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5008	1851

prune178.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	86	13	99

Error

0.1b

Counts

99 → 13

Compiler

Compiled 3954 to 1848 computations (53.3% saved)

regimes640.0ms (6.3%)

Accuracy

Total 0.3b remaining (68.9%)

Threshold costs 0.3b (68.9%)

Compiler

Compiled 7203 to 4295 computations (40.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end1.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

sample4.3s (42.7%)

Algorithm

1×

intervals

Results

1.6s	3545×	body	1024	valid
920.0ms	1173×	body	2048	valid
411.0ms	1379×	body	512	valid
121.0ms	1324×	body	128	valid
112.0ms	579×	body	256	valid

Compiler

Compiled 452 to 296 computations (34.5% saved)

Details

analyze150.0ms (1.5%)

sample77.0ms (0.8%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite43.0ms (0.4%)

series201.0ms (2%)

simplify57.0ms (0.6%)

prune49.0ms (0.5%)

localize12.0ms (0.1%)

rewrite173.0ms (1.7%)

series902.0ms (8.9%)

simplify102.0ms (1%)

prune166.0ms (1.6%)

localize20.0ms (0.2%)

rewrite138.0ms (1.4%)

series1.2s (11.6%)

simplify74.0ms (0.7%)

prune206.0ms (2%)

localize24.0ms (0.2%)

rewrite167.0ms (1.6%)

series1.2s (11.8%)

simplify44.0ms (0.4%)

prune178.0ms (1.8%)

regimes640.0ms (6.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.3s (42.7%)

Profiling