Details

analyze810.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample61.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	89×	body	1024	valid
17.0ms	41×	body	2048	valid
7.0ms	43×	body	512	valid
3.0ms	59×	body	128	valid
2.0ms	23×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify96.0ms (0.8%)

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

Merged error: 35.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.4b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.6b	(tan.f64 (+.f64 x eps))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `tan-quot_binary64_1601`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `frac-sub_binary64_1451` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-sum_binary64_1577`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

2 → 27

Calls

2 calls:

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

series473.0ms (4%)

Counts

2 → 24

Calls

2 calls:

304.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
168.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 984 to 703 computations (28.6% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4986	1602
1	4986	1602

prune76.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Merged error: 0.2b

Counts

52 → 3

Compiler

Compiled 1293 to 575 computations (55.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
16×	`add-cube-cbrt_binary64_1477`
13×	`times-frac_binary64_1448`
9×	`tan-quot_binary64_1601`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-/l/_binary64_1389` `associate-l*_binary64_1383`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `frac-times_binary64_1452` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series2.3s (19%)

Counts

4 → 48

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
589.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
329.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
264.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2328 to 1655 computations (28.9% saved)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5699	4409

prune183.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	128	11	139

Merged error: 0.1b

Counts

139 → 11

Compiler

Compiled 4274 to 1732 computations (59.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 eps) (sin.f64 x))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1464`
13×	`*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`add-cube-cbrt_binary64_1477`
8×	`add-log-exp_binary64_1481`
6×	`pow1_binary64_1503`
5×	`tan-quot_binary64_1601`
4×	`times-frac_binary64_1448`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-l*_binary64_1383`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `associate-*l/_binary64_1385` `div-exp_binary64_1493`
1×	`sum-log_binary64_1533` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `associate-/l_binary64_1387` `flip3--_binary64_1446` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 72

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
6.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.9s (16.4%)

Counts

4 → 48

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
367.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
256.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
247.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2254 to 1603 computations (28.9% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4962	3371
1	4962	3371

prune153.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	119	12	131

Merged error: 0.1b

Counts

131 → 12

Compiler

Compiled 4024 to 1572 computations (60.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (tan.f64 x))
0.6b	(cbrt.f64 (tan.f64 x))
0.6b	(cbrt.f64 (tan.f64 x))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (tan.f64 eps) (cbrt.f64 (tan.f64 x)))))) (tan.f64 x))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
9×	`cbrt-prod_binary64_1473`
8×	`add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-quot_binary64_1601`
3×	`cancel-sign-sub-inv_binary64_1408` `cbrt-div_binary64_1474` `pow1/3_binary64_1524`
2×	`difference-of-squares_binary64_1411`
1×	`times-frac_binary64_1448` `sub-neg_binary64_1435` `flip3--_binary64_1446` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

4 → 54

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (tan.f64 eps) (cbrt.f64 (tan.f64 x)))))) (tan.f64 x))
2.0ms	(cbrt.f64 (tan.f64 x))
2.0ms	(cbrt.f64 (tan.f64 x))
2.0ms	(cbrt.f64 (tan.f64 x))

series1.5s (12.7%)

Counts

4 → 30

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (tan.f64 eps) (cbrt.f64 (tan.f64 x)))))) (tan.f64 x))
154.0ms	(cbrt.f64 (tan.f64 x))
147.0ms	(cbrt.f64 (tan.f64 x))
144.0ms	(cbrt.f64 (tan.f64 x))

Compiler

Compiled 1684 to 1159 computations (31.2% saved)

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5097	2222

prune102.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	84	12	96

Merged error: 0.1b

Counts

96 → 12

Compiler

Compiled 2787 to 1024 computations (63.3% saved)

regimes521.0ms (4.4%)

Compiler: Compiled 4253 to 2491 computations (41.4% saved)

bsearch78.0ms (0.7%)

Steps

Iters	Range		Point
7	1.4091341727136722e-05	0.00023762953214016572	0.00023567465200537673
8	-0.13203328251870045	-2.023346090155918e-06	-0.00018649006335741194

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	231
1	144	231

end0.0ms (0%)

sample3.1s (26.6%)

Algorithm

1×

intervals

Results

871.0ms	3463×	body	1024	valid
547.0ms	1243×	body	2048	valid
215.0ms	1380×	body	512	valid
67.0ms	1326×	body	128	valid
59.0ms	583×	body	256	valid
4.0ms	5×	body	4096	valid

Compiler

Compiled 1557 to 912 computations (41.4% saved)

Details

analyze810.0ms (6.8%)

sample61.0ms (0.5%)

simplify96.0ms (0.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite12.0ms (0.1%)

series473.0ms (4%)

simplify72.0ms (0.6%)

prune76.0ms (0.6%)

localize11.0ms (0.1%)

rewrite39.0ms (0.3%)

series2.3s (19%)

simplify69.0ms (0.6%)

prune183.0ms (1.5%)

localize14.0ms (0.1%)

rewrite41.0ms (0.3%)

series1.9s (16.4%)

simplify88.0ms (0.7%)

prune153.0ms (1.3%)

localize14.0ms (0.1%)

rewrite25.0ms (0.2%)

series1.5s (12.7%)

simplify45.0ms (0.4%)

prune102.0ms (0.9%)

regimes521.0ms (4.4%)

bsearch78.0ms (0.7%)

simplify5.0ms (0%)

end0.0ms (0%)

sample3.1s (26.6%)

Profiling