Details

analyze788.0ms (4.4%)

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)

sample87.0ms (0.5%)

Algorithm

1×

intervals

Results

36.0ms	114×	body	1024	valid
26.0ms	40×	body	2048	valid
11.0ms	40×	body	512	valid
2.0ms	48×	body	128	valid
2.0ms	1×	body	4096	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify172.0ms (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

Merged error: 37.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.6b	(tan.f64 (+.f64 x eps))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
4×	`add-log-exp_binary64_1494` `tan-quot_binary64_1614`
3×	`add-cube-cbrt_binary64_1490` `cancel-sign-sub-inv_binary64_1421`
2×	`tan-sum_binary64_1590` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `frac-sub_binary64_1464` `add-exp-log_binary64_1493`
1×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459`

Counts

2 → 27

Calls

2 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series338.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

209.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
130.0ms	(tan.f64 (+.f64 x eps))

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune79.0ms (0.4%)

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

Merged error: 15.5b

Counts

34 → 8

Compiler

Compiled 1175 to 593 computations (49.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(/.f64 (+.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))
3.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_1455`
23×	`add-sqr-sqrt_binary64_1477`
16×	`add-cube-cbrt_binary64_1490`
13×	`times-frac_binary64_1461`
8×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
7×	`tan-quot_binary64_1614`
6×	`pow1_binary64_1516`
4×	`distribute-lft-out_binary64_1406` `cancel-sign-sub-inv_binary64_1421` `associate-/l*_binary64_1400`
3×	`associate-r_binary64_1395` `associate-/l/_binary64_1402` `associate-/r_binary64_1399` `flip--_binary64_1430` `flip3--_binary64_1459` `associate-l*_binary64_1396`
2×	`associate-/r/_binary64_1401` `difference-of-squares_binary64_1424` `diff-log_binary64_1547` `sub-neg_binary64_1448`
1×	`prod-exp_binary64_1504` `associate-r/_binary64_1397` `distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `div-exp_binary64_1506` `clear-num_binary64_1454` `frac-times_binary64_1465` `-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `cbrt-unprod_binary64_1488` `frac-sub_binary64_1464` `flip3-+_binary64_1458` `div-inv_binary64_1452` `frac-add_binary64_1463` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 87

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
10.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (11%)

Counts

4 → 12

Calls

4 calls:

990.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
549.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
212.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
209.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5820	2593

prune983.0ms (5.5%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	80	19	99
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	85	22	107

Merged error: 15.3b

Counts

107 → 22

Compiler

Compiled 20754 to 10478 computations (49.5% saved)

localize15.0ms (0.1%)

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))
3.0b	(-.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))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1477`
12×	`*-un-lft-identity_binary64_1455`
10×	`add-cube-cbrt_binary64_1490`
9×	`add-log-exp_binary64_1494`
7×	`pow1_binary64_1516`
6×	`add-cbrt-cube_binary64_1491` `exp-prod_binary64_1507` `add-exp-log_binary64_1493`
5×	`tan-quot_binary64_1614` `cancel-sign-sub-inv_binary64_1421` `log-prod_binary64_1541`
4×	`exp-sum_binary64_1501` `log-pow_binary64_1544`
3×	`associate-r_binary64_1395` `sub-neg_binary64_1448` `associate-l_binary64_1396`
2×	`difference-of-squares_binary64_1424` `exp-diff_binary64_1503` `diff-log_binary64_1547` `rem-exp-log_binary64_1495`
1×	`prod-exp_binary64_1504` `associate-r/_binary64_1397` `distribute-lft-out--_binary64_1407` `log-div_binary64_1542` `frac-times_binary64_1465` `-commutative_binary64_1386` `flip--_binary64_1430` `cbrt-unprod_binary64_1488` `frac-sub_binary64_1464` `times-frac_binary64_1461` `flip3--_binary64_1459` `rem-log-exp_binary64_1496` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 72

Calls

4 calls:

21.0ms	(-.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))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
4.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

series2.0s (11.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.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))
377.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
291.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
191.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4979	1698
1	4979	1698

prune272.0ms (1.5%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	85	21	106

Merged error: 15.3b

Counts

106 → 21

Compiler

Compiled 5899 to 2799 computations (52.6% saved)

localize20.0ms (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) (tan.f64 eps))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.0b	(-.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))

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`tan-quot_binary64_1614`
14×	`add-sqr-sqrt_binary64_1477`
11×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
10×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
6×	`associate-r_binary64_1395` `add-log-exp_binary64_1494` `associate-l_binary64_1396`
5×	`associate-*r/_binary64_1397` `frac-times_binary64_1465` `frac-sub_binary64_1464`
4×	`associate-*l/_binary64_1398`
3×	`prod-exp_binary64_1504` `cube-div_binary64_1484` `cancel-sign-sub-inv_binary64_1421` `cbrt-unprod_binary64_1488` `pow-unpow_binary64_1532` `pow-prod-down_binary64_1526`
2×	`flip-+_binary64_1429` `*-commutative_binary64_1386` `pow-pow_binary64_1527` `associate--l+_binary64_1392` `rem-cube-cbrt_binary64_1478` `flip3-+_binary64_1458` `pow-exp_binary64_1523` `unswap-sqr_binary64_1423`
1×	`distribute-rgt-in_binary64_1405` `cube-mult_binary64_1485` `unpow3_binary64_1521` `unpow-prod-down_binary64_1534` `pow-to-exp_binary64_1524` `sqr-pow_binary64_1427` `flip--_binary64_1430` `diff-log_binary64_1547` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `cube-prod_binary64_1483` `flip3--_binary64_1459`

Counts

4 → 88

Calls

4 calls:

26.0ms	(-.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))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

series7.1s (39.6%)

Counts

4 → 12

Calls

4 calls:

6.4s	(-.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))
326.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
189.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
173.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5054	3333

prune365.0ms (2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	4	15	19
Picked	1	0	1
Done	0	1	1
Total	100	21	121

Merged error: 15.2b

Counts

121 → 21

Compiler

Compiled 9619 to 4251 computations (55.8% saved)

regimes129.0ms (0.7%)

Compiler: Compiled 1386 to 766 computations (44.7% saved)

bsearch63.0ms (0.4%)

Steps

Iters	Range		Point
6	3.0876816840121187e-115	1.9489484085498834e-114	1.914951132073428e-114
6	-2.70031633841226e-53	-2.8742722130247817e-54	-2.5441009276949707e-53

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	53
1	59	53

end0.0ms (0%)

sample2.9s (16.5%)

Algorithm

1×

intervals

Results

1.0s	3537×	body	1024	valid
833.0ms	1220×	body	2048	valid
225.0ms	1400×	body	512	valid
65.0ms	1244×	body	128	valid
61.0ms	595×	body	256	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 743 to 417 computations (43.9% saved)

Details

analyze788.0ms (4.4%)

sample87.0ms (0.5%)

simplify172.0ms (1%)

prune2.0ms (0%)

localize8.0ms (0%)

rewrite15.0ms (0.1%)

series338.0ms (1.9%)

simplify125.0ms (0.7%)

prune79.0ms (0.4%)

localize13.0ms (0.1%)

rewrite44.0ms (0.2%)

series2.0s (11%)

simplify78.0ms (0.4%)

prune983.0ms (5.5%)

localize15.0ms (0.1%)

rewrite42.0ms (0.2%)

series2.0s (11.3%)

simplify75.0ms (0.4%)

prune272.0ms (1.5%)

localize20.0ms (0.1%)

rewrite62.0ms (0.4%)

series7.1s (39.6%)

simplify62.0ms (0.3%)

prune365.0ms (2%)

regimes129.0ms (0.7%)

bsearch63.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (16.5%)

Profiling