Details

analyze1.4s (13.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample184.0ms (1.7%)

Algorithm

1×

intervals

Results

114.0ms	61×	body	2048	valid
38.0ms	98×	body	1024	valid
9.0ms	44×	body	512	valid
5.0ms	5×	body	4096	valid
4.0ms	32×	body	256	valid
1.0ms	16×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify175.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune4.0ms (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

33.8b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

1.9b	(-.f64 x (sin.f64 x))
1.9b	(-.f64 x (tan.f64 x))
0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.9b	(-.f64 x (tan.f64 x))
1.9b	(-.f64 x (sin.f64 x))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

6 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
0.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0ms	(-.f64 x (tan.f64 x))

series230.0ms (2.2%)

Counts

3 → 26

Calls

3 calls:

113.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
66.0ms	(-.f64 x (tan.f64 x))
51.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 549 to 391 computations (28.8% saved)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4924	2050
1	4924	2050

prune126.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

0.0b

Counts

111 → 4

Compiler

Compiled 1812 to 442 computations (75.6% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

15.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
0.3b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.3b	(.f64 (.f64 x x) 9/40)
15.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 60

Calls

6 calls:

8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)
0.0ms	(*.f64 27/2800 (pow.f64 x 4))
0.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series104.0ms (1%)

Counts

3 → 11

Calls

3 calls:

44.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
33.0ms	(*.f64 27/2800 (pow.f64 x 4))
27.0ms	(.f64 (.f64 x x) 9/40)

Compiler

Compiled 222 to 201 computations (9.5% saved)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5410	860

prune76.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Compiler

Compiled 1224 to 888 computations (27.5% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

15.3b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
0.3b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.3b	(.f64 (.f64 x x) 9/40)
15.3b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `associate--l+_binary64`
3×	`pow-prod-down_binary64` `diff-log_binary64`
2×	`sub-neg_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

3 → 62

Calls

6 calls:

10.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
6.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
0.0ms	(*.f64 27/2800 (pow.f64 x 4))
0.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

series97.0ms (0.9%)

Counts

3 → 11

Calls

3 calls:

37.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
35.0ms	(*.f64 27/2800 (pow.f64 x 4))
25.0ms	(.f64 (.f64 x x) 9/40)

Compiler

Compiled 222 to 201 computations (9.5% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4875	881
1	4875	881

prune72.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	73	4	77

Error

0.0b

Counts

77 → 4

Compiler

Compiled 1242 to 891 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.9b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
1.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
1.9b	(-.f64 x (tan.f64 x))
1.9b	(-.f64 x (tan.f64 x))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
21×	`distribute-lft-out--_binary64`
15×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 118

Calls

8 calls:

35.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
0.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

series321.0ms (3%)

Counts

4 → 32

Calls

4 calls:

155.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
61.0ms	(-.f64 x (tan.f64 x))
60.0ms	(-.f64 x (tan.f64 x))
45.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))

Compiler

Compiled 810 to 565 computations (30.2% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5367	2805

prune114.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	151	3	154

Error

0.0b

Counts

154 → 3

Compiler

Compiled 2997 to 562 computations (81.2% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	209	570
1	209	570

regimes130.0ms (1.2%)

Compiler: Compiled 788 to 490 computations (37.8% saved)

bsearch57.0ms (0.5%)

Steps

Iters	Range		Point
7	0.0008729951881598737	0.14829432703029602	0.02883492941991452
10	-20396235690.07604	-4.2447522135263546e-07	-0.03249701931273373

Compiler

Compiled 1 to 1 computations (0% saved)

regimes119.0ms (1.1%)

Compiler: Compiled 678 to 458 computations (32.4% saved)

bsearch48.0ms (0.5%)

Steps

Iters	Range		Point
7	0.0008729951881598737	0.14829432703029602	0.02883492941991452
10	-20396235690.07604	-4.2447522135263546e-07	-0.03249701931273373

Compiler

Compiled 1 to 1 computations (0% saved)

regimes70.0ms (0.7%)

Compiler: Compiled 231 to 188 computations (18.6% saved)

bsearch44.0ms (0.4%)

Steps

Iters	Range		Point
7	0.0008729951881598737	0.14829432703029602	0.027931797038213965
10	-20396235690.07604	-4.2447522135263546e-07	-0.027646303307784493

Compiler

Compiled 1 to 1 computations (0% saved)

regimes56.0ms (0.5%)

Compiler: Compiled 178 to 146 computations (18% saved)

bsearch44.0ms (0.4%)

Steps

Iters	Range		Point
7	0.0008729951881598737	0.14829432703029602	0.027931797038213965
10	-20396235690.07604	-4.2447522135263546e-07	-0.027646303307784493

Compiler

Compiled 1 to 1 computations (0% saved)

regimes30.0ms (0.3%)

Compiler: Compiled 51 to 46 computations (9.8% saved)

bsearch50.0ms (0.5%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	2.8145701106272707
10	-20396235690.07604	-4.2447522135263546e-07	-2.7411376912888787

Compiler

Compiled 1 to 1 computations (0% saved)

regimes26.0ms (0.2%)

Compiler: Compiled 25 to 24 computations (4% saved)

bsearch49.0ms (0.5%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	2.241160692489287
10	-20396235690.07604	-4.2447522135263546e-07	-2.3082717611940438

Compiler

Compiled 1 to 1 computations (0% saved)

regimes22.0ms (0.2%)

Compiler: Compiled 19 to 20 computations (-5.3% saved)

bsearch48.0ms (0.4%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	2.5597214803437227
10	-20396235690.07604	-4.2447522135263546e-07	-2.3082717611940438

Compiler

Compiled 1 to 1 computations (0% saved)

regimes23.0ms (0.2%)

Compiler: Compiled 13 to 16 computations (-23.1% saved)

bsearch45.0ms (0.4%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	2.5597214803437227
10	-20396235690.07604	-4.2447522135263546e-07	-2.63292120876517

Compiler

Compiled 1 to 1 computations (0% saved)

regimes21.0ms (0.2%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch41.0ms (0.4%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	1.5790270068921035
10	-20396235690.07604	-4.2447522135263546e-07	-1.558945226716624

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.2%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch44.0ms (0.4%)

Steps

Iters	Range		Point
10	0.14829432703029602	970114620.7492073	1.5790270068921035
10	-20396235690.07604	-4.2447522135263546e-07	-1.558945226716624

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.1%)

Accuracy

Total 0.0b remaining (51%)

Threshold costs 0.0b (51%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch15.0ms (0.1%)

Compiler: Compiled 341 to 190 computations (44.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	466
1	156	466

end0.0ms (0%)

sample6.2s (58.6%)

Algorithm

1×

intervals

Results

3.7s	1933×	body	2048	valid
1.0s	3029×	body	1024	valid
289.0ms	1526×	body	512	valid
125.0ms	115×	body	4096	valid
109.0ms	776×	body	256	valid
50.0ms	621×	body	128	valid

Compiler

Compiled 683 to 423 computations (38.1% saved)

Pareto

0.9819623917990712

Details

analyze1.4s (13.4%)

sample184.0ms (1.7%)

simplify175.0ms (1.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite28.0ms (0.3%)

series230.0ms (2.2%)

simplify63.0ms (0.6%)

prune126.0ms (1.2%)

localize8.0ms (0.1%)

rewrite24.0ms (0.2%)

series104.0ms (1%)

simplify61.0ms (0.6%)

prune76.0ms (0.7%)

localize8.0ms (0.1%)

rewrite27.0ms (0.3%)

series97.0ms (0.9%)

simplify75.0ms (0.7%)

prune72.0ms (0.7%)

localize9.0ms (0.1%)

rewrite61.0ms (0.6%)

series321.0ms (3%)

simplify75.0ms (0.7%)

prune114.0ms (1.1%)

simplify11.0ms (0.1%)

regimes130.0ms (1.2%)

bsearch57.0ms (0.5%)

regimes119.0ms (1.1%)

bsearch48.0ms (0.5%)

regimes70.0ms (0.7%)

bsearch44.0ms (0.4%)

regimes56.0ms (0.5%)

bsearch44.0ms (0.4%)

regimes30.0ms (0.3%)

bsearch50.0ms (0.5%)

regimes26.0ms (0.2%)

bsearch49.0ms (0.5%)

regimes22.0ms (0.2%)

bsearch48.0ms (0.4%)

regimes23.0ms (0.2%)

bsearch45.0ms (0.4%)

regimes21.0ms (0.2%)

bsearch41.0ms (0.4%)

regimes17.0ms (0.2%)

bsearch44.0ms (0.4%)

regimes7.0ms (0.1%)

bsearch15.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample6.2s (58.6%)

Profiling