Details

analyze907.0ms (6.5%)

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
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)

sample65.0ms (0.5%)

Algorithm

1×

intervals

Results

28.0ms	115×	body	1024	valid
15.0ms	38×	body	2048	valid
7.0ms	42×	body	512	valid
2.0ms	46×	body	128	valid
1.0ms	15×	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

prune3.0ms (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

39.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.5b	(tan.f64 (+.f64 x eps))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

22.6b

Rules

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

Compiler

Compiled 416 to 108 computations (74% saved)

series477.0ms (3.4%)

Error

14.3b

Counts

2 → 22

Calls

2 calls:

276.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
162.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1514 to 887 computations (41.4% saved)

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5606	1292

prune64.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

0.2b

Counts

50 → 4

Compiler

Compiled 1094 to 412 computations (62.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite138.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `associate-r_binary64_1382` `associate-/l/_binary64_1389` `associate-/r*_binary64_1386`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `frac-sub_binary64_1451` `sub-neg_binary64_1435` `distribute-lft-out--_binary64_1394` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-times_binary64_1452` `unswap-sqr_binary64_1410` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `*-commutative_binary64_1373` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `sum-log_binary64_1533` `+-commutative_binary64_1372`

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))))
7.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2365 to 732 computations (69% saved)

series1.8s (13.2%)

Error

0.2b

Counts

4 → 40

Calls

4 calls:

882.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
500.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
212.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
192.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3162 to 1710 computations (45.9% saved)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5018	3663

prune161.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Error

0.1b

Counts

132 → 10

Compiler

Compiled 3719 to 1267 computations (65.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
4.6b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite236.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

30×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
20×	`add-sqr-sqrt_binary64_1464`
18×	`*-un-lft-identity_binary64_1442`
13×	`add-cube-cbrt_binary64_1477` `cancel-sign-sub-inv_binary64_1408`
12×	`times-frac_binary64_1448`
9×	`add-log-exp_binary64_1481` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
8×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
6×	`pow1_binary64_1503`
3×	`frac-sub_binary64_1451` `div-inv_binary64_1439` `sin-mult_binary64_1597` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389` `cos-mult_binary64_1596` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
1×	`sum-log_binary64_1533` `frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `distribute-lft-out_binary64_1393` `associate--l+_binary64_1379` `pow-prod-down_binary64_1513` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 98

Calls

4 calls:

30.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 6105 to 1482 computations (75.7% saved)

series1.4s (10.4%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

928.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
204.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
195.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
76.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 3658 to 1650 computations (54.9% saved)

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5019	4583

prune204.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Error

0.1b

Counts

137 → 9

Compiler

Compiled 7105 to 1906 computations (73.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
4.5b	(+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (-.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 x) (cos.f64 x))))

rewrite234.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

30×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
18×	`*-un-lft-identity_binary64_1442`
15×	`add-sqr-sqrt_binary64_1464`
14×	`associate-+r+_binary64_1374`
13×	`add-cube-cbrt_binary64_1477` `cancel-sign-sub-inv_binary64_1408`
11×	`times-frac_binary64_1448`
9×	`add-log-exp_binary64_1481` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
8×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
6×	`pow1_binary64_1503`
3×	`frac-add_binary64_1450` `div-inv_binary64_1439` `sin-mult_binary64_1597` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389` `cos-mult_binary64_1596` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
1×	`diff-log_binary64_1534` `frac-sub_binary64_1451` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out--_binary64_1394` `associate-+r-_binary64_1376` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 97

Calls

4 calls:

35.0ms	(+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (-.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 x) (cos.f64 x))))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 5846 to 1411 computations (75.9% saved)

series1.4s (10.3%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

924.0ms	(+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (-.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 x) (cos.f64 x))))
204.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
188.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
82.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 3658 to 1650 computations (54.9% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5299	4906

prune184.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	126	9	135

Error

0.1b

Counts

135 → 9

Compiler

Compiled 6573 to 1687 computations (74.3% saved)

regimes1.4s (9.9%)

Accuracy

Total 0.2b remaining (66.2%)

Threshold costs 0.2b (66.2%)

Compiler

Compiled 10364 to 5617 computations (45.8% saved)

bsearch101.0ms (0.7%)

Steps

Iters	Range		Point
9	1.0762346048139389e-05	2.2304107085495852	2.2886471627852177e-05
11	-20292776.65736414	-1.1731026528524935e-14	-5.846200722042183e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	459	194
1	459	194

end0.0ms (0%)

sample4.6s (33.2%)

Algorithm

1×

intervals

Results

911.0ms	3534×	body	1024	valid
555.0ms	1157×	body	2048	valid
215.0ms	1359×	body	512	valid
66.0ms	1335×	body	128	valid
61.0ms	611×	body	256	valid
4.0ms	4×	body	4096	valid

Compiler

Compiled 3562 to 1936 computations (45.6% saved)

Details

analyze907.0ms (6.5%)

sample65.0ms (0.5%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite39.0ms (0.3%)

series477.0ms (3.4%)

simplify37.0ms (0.3%)

prune64.0ms (0.5%)

localize11.0ms (0.1%)

rewrite138.0ms (1%)

series1.8s (13.2%)

simplify63.0ms (0.5%)

prune161.0ms (1.2%)

localize21.0ms (0.1%)

rewrite236.0ms (1.7%)

series1.4s (10.4%)

simplify94.0ms (0.7%)

prune204.0ms (1.5%)

localize21.0ms (0.1%)

rewrite234.0ms (1.7%)

series1.4s (10.3%)

simplify77.0ms (0.6%)

prune184.0ms (1.3%)

regimes1.4s (9.9%)

bsearch101.0ms (0.7%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample4.6s (33.2%)

Profiling