Details

analyze783.0ms (5.2%)

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)

sample62.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	100×	body	1024	valid
17.0ms	42×	body	2048	valid
7.0ms	48×	body	512	valid
2.0ms	24×	body	256	valid
2.0ms	42×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify98.0ms (0.6%)

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

36.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.8b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (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))

series175.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

112.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
63.0ms	(tan.f64 (+.f64 x eps))

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune40.0ms (0.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Error

14.9b

Counts

34 → 8

Compiler

Compiled 567 to 180 computations (68.3% saved)

localize10.0ms (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))
2.8b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite43.0ms (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:

15.0ms	(-.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))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.0s (6.7%)

Counts

4 → 12

Calls

4 calls:

522.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
286.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
105.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
99.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5619	2567

prune134.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	86	14	100
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	92	16	108

Error

14.8b

Counts

108 → 16

Compiler

Compiled 2961 to 1008 computations (66% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
2.6b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite71.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`pow1_binary64_1503`
45×	`tan-quot_binary64_1601`
21×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `frac-times_binary64_1452`
19×	`pow-prod-down_binary64_1513`
15×	`associate-*r/_binary64_1384`
14×	`associate-*l/_binary64_1385`
10×	`cbrt-unprod_binary64_1475` `add-sqr-sqrt_binary64_1464` `prod-exp_binary64_1491`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`add-log-exp_binary64_1481`
5×	`frac-sub_binary64_1451`
4×	`associate-r_binary64_1382` `associate-l_binary64_1383` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
3×	`cancel-sign-sub-inv_binary64_1408` `pow-unpow_binary64_1519` `cube-div_binary64_1471`
2×	`associate--l+_binary64_1379` `pow-exp_binary64_1510` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `rem-cube-cbrt_binary64_1465` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-pow_binary64_1514`
1×	`pow2_binary64_1523` `cube-mult_binary64_1472` `swap-sqr_binary64_1409` `sub-neg_binary64_1435` `flip3--_binary64_1446` `cube-prod_binary64_1470` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-rgt-in_binary64_1392` `unpow-prod-down_binary64_1521` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 116

Calls

4 calls:

25.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
15.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.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)

series4.2s (27.9%)

Counts

4 → 12

Calls

4 calls:

3.8s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
187.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
160.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5035	3722

prune266.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	129	15	144

Error

14.8b

Counts

144 → 15

Compiler

Compiled 6921 to 2712 computations (60.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (cos.f64 eps) 2)
0.3b	(pow.f64 (sin.f64 eps) 2)
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
2.6b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (/.f64 (.f64 (tan.f64 x) (.f64 (sin.f64 x) (pow.f64 (sin.f64 eps) 2))) (.f64 (cos.f64 x) (pow.f64 (cos.f64 eps) 2))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`pow-unpow_binary64_1519` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-quot_binary64_1601`
7×	`add-cbrt-cube_binary64_1478` `unpow-prod-down_binary64_1521`
6×	`add-log-exp_binary64_1481`
5×	`frac-sub_binary64_1451`
4×	`pow-exp_binary64_1510` `pow-pow_binary64_1514`
3×	`associate-*r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `frac-times_binary64_1452` `sqr-pow_binary64_1414` `cube-div_binary64_1471` `pow-to-exp_binary64_1511`
2×	`associate--l+_binary64_1379` `unpow2_binary64_1507` `rem-cube-cbrt_binary64_1465` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-*l/_binary64_1385`
1×	`cube-mult_binary64_1472` `cbrt-unprod_binary64_1475` `sub-neg_binary64_1435` `flip3--_binary64_1446` `cube-prod_binary64_1470` `pow-prod-down_binary64_1513` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `unpow3_binary64_1508` `distribute-rgt-in_binary64_1392` `prod-exp_binary64_1491`

Counts

4 → 82

Calls

4 calls:

31.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (/.f64 (.f64 (tan.f64 x) (.f64 (sin.f64 x) (pow.f64 (sin.f64 eps) 2))) (.f64 (cos.f64 x) (pow.f64 (cos.f64 eps) 2))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.0ms	(pow.f64 (sin.f64 eps) 2)
2.0ms	(pow.f64 (cos.f64 eps) 2)

series4.1s (27.3%)

Counts

4 → 12

Calls

4 calls:

3.9s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (/.f64 (.f64 (tan.f64 x) (.f64 (sin.f64 x) (pow.f64 (sin.f64 eps) 2))) (.f64 (cos.f64 x) (pow.f64 (cos.f64 eps) 2))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
190.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
14.0ms	(pow.f64 (sin.f64 eps) 2)
12.0ms	(pow.f64 (cos.f64 eps) 2)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5093	3769

prune226.0ms (1.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	94	15	109

Error

14.8b

Counts

109 → 15

Compiler

Compiled 5923 to 2666 computations (55% saved)

regimes377.0ms (2.5%)

Accuracy

Total 0.9b remaining (5.6%)

Threshold costs 0.9b (5.6%)

Compiler

Compiled 4029 to 2212 computations (45.1% saved)

bsearch75.0ms (0.5%)

Steps

Iters	Range		Point
7	1.8438654255481383e-60	1.633205598528326e-58	1.6694113497634884e-59
10	-4.2149623711150614e-17	-5.817536317265985e-29	-7.780852968026817e-23

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	546	141
1	546	141

end0.0ms (0%)

sample2.9s (19%)

Algorithm

1×

intervals

Results

869.0ms	3550×	body	1024	valid
530.0ms	1223×	body	2048	valid
203.0ms	1346×	body	512	valid
61.0ms	611×	body	256	valid
59.0ms	1269×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 1433 to 781 computations (45.5% saved)

Details

analyze783.0ms (5.2%)

sample62.0ms (0.4%)

simplify98.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite13.0ms (0.1%)

series175.0ms (1.2%)

simplify96.0ms (0.6%)

prune40.0ms (0.3%)

localize10.0ms (0.1%)

rewrite43.0ms (0.3%)

series1.0s (6.7%)

simplify88.0ms (0.6%)

prune134.0ms (0.9%)

localize19.0ms (0.1%)

rewrite71.0ms (0.5%)

series4.2s (27.9%)

simplify97.0ms (0.6%)

prune266.0ms (1.8%)

localize33.0ms (0.2%)

rewrite57.0ms (0.4%)

series4.1s (27.3%)

simplify87.0ms (0.6%)

prune226.0ms (1.5%)

regimes377.0ms (2.5%)

bsearch75.0ms (0.5%)

simplify23.0ms (0.2%)

end0.0ms (0%)

sample2.9s (19%)

Profiling