Details

analyze2.0ms (0%)

Algorithm

1×

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)

sample92.0ms (1%)

Algorithm

1×

intervals

Results

45.0ms	120×	body	1024	valid
21.0ms	34×	body	2048	valid
10.0ms	46×	body	512	valid
3.0ms	40×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify106.0ms (1.1%)

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

34.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.9b	(sin.f64 (+.f64 x eps))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

20.1b

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:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series169.0ms (1.7%)

Error

12.5b

Counts

2 → 22

Calls

2 calls:

93.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
39.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 616 to 371 computations (39.8% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4896	675
1	4896	675

prune93.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

0.3b

Counts

49 → 4

Compiler

Compiled 617 to 201 computations (67.4% saved)

localize22.0ms (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))
0.1b	(*.f64 (cos.f64 eps) (sin.f64 x))
3.4b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite97.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

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:

11.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
7.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
5.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
4.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1495 to 285 computations (80.9% saved)

series614.0ms (6.4%)

Error

0.3b

Counts

4 → 40

Calls

4 calls:

209.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
158.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
123.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
97.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1642 to 899 computations (45.2% saved)

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4968	1775
1	4968	1775

prune155.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Error

0.1b

Counts

110 → 12

Compiler

Compiled 2216 to 646 computations (70.8% saved)

localize23.0ms (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))
0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
1.2b	(+.f64 (cos.f64 eps) -1)

rewrite117.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64_1464`
12×	`*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-cube-cbrt_binary64_1477` `associate-r_binary64_1382`
6×	`associate-l_binary64_1383`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`sum-log_binary64_1533` `difference-of-sqr--1_binary64_1413` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-r/_binary64_1384` `-commutative_binary64_1373` `associate-+r+_binary64_1374`

Counts

4 → 68

Calls

4 calls:

8.0ms	(+.f64 (cos.f64 eps) -1)
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))

Compiler

Compiled 1405 to 554 computations (60.6% saved)

series505.0ms (5.2%)

Error

0.1b

Counts

4 → 31

Calls

4 calls:

224.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
132.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
102.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
18.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1329 to 865 computations (34.9% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5209	1469

prune144.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	11	99
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Error

0.0b

Counts

111 → 13

Compiler

Compiled 2086 to 880 computations (57.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))) (-.f64 (cos.f64 eps) -1))
0.2b	(.f64 (sin.f64 x) (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))))
0.2b	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
0.4b	(-.f64 (cos.f64 eps) -1)

rewrite140.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
18×	`*-un-lft-identity_binary64_1442`
12×	`add-cube-cbrt_binary64_1477`
11×	`pow1_binary64_1503` `associate-r_binary64_1382`
7×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
6×	`add-log-exp_binary64_1481` `associate-l_binary64_1383`
5×	`distribute-rgt-neg-out_binary64_1402` `times-frac_binary64_1448` `associate-/r*_binary64_1386`
4×	`pow-prod-down_binary64_1513`
3×	`difference-of-squares_binary64_1411` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-out--_binary64_1394` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `*-commutative_binary64_1373` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `unswap-sqr_binary64_1410` `neg-mul-1_binary64_1438` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `distribute-frac-neg_binary64_1405` `associate-/l*_binary64_1387`

Counts

4 → 91

Calls

4 calls:

11.0ms	(.f64 (sin.f64 x) (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))))
11.0ms	(/.f64 (.f64 (sin.f64 x) (.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 2495 to 729 computations (70.8% saved)

series549.0ms (5.7%)

Error

0.0b

Counts

4 → 23

Calls

4 calls:

281.0ms	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))) (-.f64 (cos.f64 eps) -1))
179.0ms	(.f64 (sin.f64 x) (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))))
43.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
23.0ms	(-.f64 (cos.f64 eps) -1)

Compiler

Compiled 1407 to 942 computations (33% saved)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4952	1562
1	4952	1562

prune144.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	114	13	127

Error

0.0b

Counts

127 → 13

Compiler

Compiled 2523 to 1002 computations (60.3% saved)

regimes717.0ms (7.4%)

Accuracy

Total 0.3b remaining (89.3%)

Threshold costs 0.3b (89.3%)

Compiler

Compiled 7286 to 4484 computations (38.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	31
1	58	31

end0.0ms (0%)

sample5.5s (57.1%)

Algorithm

1×

intervals

Results

1.2s	3530×	body	1024	valid
746.0ms	1189×	body	2048	valid
304.0ms	1391×	body	512	valid
98.0ms	1317×	body	128	valid
90.0ms	571×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 2447 to 1513 computations (38.2% saved)

Details

analyze2.0ms (0%)

sample92.0ms (1%)

simplify106.0ms (1.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite58.0ms (0.6%)

series169.0ms (1.7%)

simplify114.0ms (1.2%)

prune93.0ms (1%)

localize22.0ms (0.2%)

rewrite97.0ms (1%)

series614.0ms (6.4%)

simplify75.0ms (0.8%)

prune155.0ms (1.6%)

localize23.0ms (0.2%)

rewrite117.0ms (1.2%)

series505.0ms (5.2%)

simplify92.0ms (1%)

prune144.0ms (1.5%)

localize14.0ms (0.1%)

rewrite140.0ms (1.4%)

series549.0ms (5.7%)

simplify88.0ms (0.9%)

prune144.0ms (1.5%)

regimes717.0ms (7.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.5s (57.1%)

Profiling