Details

analyze1.0s (6.2%)

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)

sample67.0ms (0.4%)

Algorithm

1×

intervals

Results

28.0ms	102×	body	1024	valid
17.0ms	38×	body	2048	valid
8.0ms	44×	body	512	valid
3.0ms	48×	body	128	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify141.0ms (0.8%)

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

35.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.2b	(tan.f64 (+.f64 x eps))

rewrite15.0ms (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:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series239.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

126.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
113.0ms	(tan.f64 (+.f64 x eps))

simplify117.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune47.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Error

13.2b

Counts

34 → 7

Compiler

Compiled 555 to 172 computations (69% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.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))
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1464`
11×	`*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
7×	`tan-quot_binary64_1601` `add-cube-cbrt_binary64_1477`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`cancel-sign-sub-inv_binary64_1408`
3×	`associate-r_binary64_1382` `associate-l_binary64_1383`
2×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `times-frac_binary64_1448` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `frac-add_binary64_1450` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 64

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series1.2s (7%)

Counts

4 → 12

Calls

4 calls:

722.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
156.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
152.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
136.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5520	1595

prune189.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Error

13.0b

Counts

83 → 12

Compiler

Compiled 2111 to 734 computations (65.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1464`
12×	`*-un-lft-identity_binary64_1442`
10×	`add-cube-cbrt_binary64_1477`
9×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `exp-prod_binary64_1494`
5×	`log-prod_binary64_1528` `cancel-sign-sub-inv_binary64_1408` `tan-quot_binary64_1601`
4×	`log-pow_binary64_1531` `exp-sum_binary64_1488`
3×	`associate-r_binary64_1382` `sub-neg_binary64_1435` `associate-l_binary64_1383`
2×	`rem-exp-log_binary64_1482` `diff-log_binary64_1534` `exp-diff_binary64_1490` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `times-frac_binary64_1448` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `frac-times_binary64_1452` `prod-exp_binary64_1491` `log-div_binary64_1529` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 72

Calls

4 calls:

30.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
4.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))

series1.4s (8.5%)

Counts

4 → 12

Calls

4 calls:

806.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
304.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
182.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
129.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5003	1698

prune142.0ms (0.8%)

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

Error

13.0b

Counts

96 → 12

Compiler

Compiled 2349 to 879 computations (62.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))

rewrite130.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`tan-quot_binary64_1601`
20×	`add-sqr-sqrt_binary64_1464`
14×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
11×	`associate-r/_binary64_1384` `frac-times_binary64_1452` `-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
6×	`associate-l_binary64_1383` `add-log-exp_binary64_1481`
5×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `associate-*l/_binary64_1385`
4×	`associate-r_binary64_1382` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416`
3×	`cancel-sign-sub-inv_binary64_1408` `times-frac_binary64_1448` `pow-unpow_binary64_1519` `cube-div_binary64_1471` `difference-of-squares_binary64_1411`
2×	`pow-exp_binary64_1510` `*-commutative_binary64_1373` `rem-cube-cbrt_binary64_1465` `pow-pow_binary64_1514`
1×	`cube-mult_binary64_1472` `sub-neg_binary64_1435` `flip3--_binary64_1446` `cube-prod_binary64_1470` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-lft-out--_binary64_1394` `unpow-prod-down_binary64_1521` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 98

Calls

4 calls:

85.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))
10.0ms	(.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

series6.1s (36.4%)

Counts

4 → 12

Calls

4 calls:

5.3s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (+.f64 1 (.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))) (tan.f64 x))
363.0ms	(.f64 (tan.f64 x) (.f64 (tan.f64 eps) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
289.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
186.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5079	3693

prune291.0ms (1.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	107	15	122

Error

13.0b

Counts

122 → 15

Compiler

Compiled 5028 to 2023 computations (59.8% saved)

regimes496.0ms (3%)

Accuracy

Total 0.9b remaining (6%)

Threshold costs 0.9b (6%)

Compiler

Compiled 3975 to 2165 computations (45.5% saved)

bsearch110.0ms (0.7%)

Steps

Iters	Range		Point
8	9.699177682519535e-44	1.7149956727172802e-40	4.0501768016039094e-42
7	-7.654708883586819e-59	-2.3600134919764452e-60	-6.951010323486192e-59

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	120	113
1	120	113

end0.0ms (0%)

sample4.5s (27.1%)

Algorithm

1×

intervals

Results

1.4s	3523×	body	1024	valid
966.0ms	1215×	body	2048	valid
310.0ms	1317×	body	512	valid
97.0ms	1320×	body	128	valid
97.0ms	624×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 1388 to 753 computations (45.7% saved)

Details

analyze1.0s (6.2%)

sample67.0ms (0.4%)

simplify141.0ms (0.8%)

prune2.0ms (0%)

localize6.0ms (0%)

rewrite15.0ms (0.1%)

series239.0ms (1.4%)

simplify117.0ms (0.7%)

prune47.0ms (0.3%)

localize18.0ms (0.1%)

rewrite38.0ms (0.2%)

series1.2s (7%)

simplify113.0ms (0.7%)

prune189.0ms (1.1%)

localize29.0ms (0.2%)

rewrite51.0ms (0.3%)

series1.4s (8.5%)

simplify110.0ms (0.7%)

prune142.0ms (0.8%)

localize19.0ms (0.1%)

rewrite130.0ms (0.8%)

series6.1s (36.4%)

simplify111.0ms (0.7%)

prune291.0ms (1.7%)

regimes496.0ms (3%)

bsearch110.0ms (0.7%)

simplify7.0ms (0%)

end0.0ms (0%)

sample4.5s (27.1%)

Profiling