Details

analyze2.2s (11.6%)

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)

sample394.0ms (2.1%)

Algorithm

1×

intervals

Results

273.0ms	64×	body	2048	valid
67.0ms	77×	body	1024	valid
19.0ms	54×	body	512	valid
8.0ms	28×	body	256	valid
5.0ms	32×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify316.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune7.0ms (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

32.1b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize17.0ms (0.1%)

Local error

Found 6 expressions with local error:

1.4b	(-.f64 x (sin.f64 x))
1.4b	(-.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)))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite62.0ms (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:

28.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
11.0ms	(-.f64 x (sin.f64 x))
7.0ms	(-.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))

series384.0ms (2%)

Counts

3 → 24

Calls

3 calls:

200.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
116.0ms	(-.f64 x (tan.f64 x))
68.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 521 to 368 computations (29.4% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5060	2135

prune239.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

0.0b

Counts

109 → 4

Compiler

Compiled 1852 to 434 computations (76.6% saved)

localize17.0ms (0.1%)

Local error

Found 6 expressions with local error:

10.8b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
10.8b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite48.0ms (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` `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:

14.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
11.0ms	(*.f64 27/2800 (pow.f64 x 4))
10.0ms	(.f64 (.f64 x x) 9/40)
0.0ms	(.f64 (.f64 x x) 9/40)
0.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series174.0ms (0.9%)

Counts

3 → 11

Calls

3 calls:

70.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
56.0ms	(*.f64 27/2800 (pow.f64 x 4))
48.0ms	(.f64 (.f64 x x) 9/40)

Compiler

Compiled 222 to 201 computations (9.5% saved)

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5410	860

prune130.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	70	5	75

Error

Counts

75 → 5

Compiler

Compiled 1231 to 897 computations (27.1% saved)

localize16.0ms (0.1%)

Local error

Found 6 expressions with local error:

10.8b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
10.8b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

rewrite44.0ms (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` `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:

16.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
10.0ms	(.f64 (.f64 x x) 9/40)
9.0ms	(*.f64 27/2800 (pow.f64 x 4))
0.0ms	(.f64 (.f64 x x) 9/40)
0.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

series172.0ms (0.9%)

Counts

3 → 11

Calls

3 calls:

60.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
58.0ms	(*.f64 27/2800 (pow.f64 x 4))
53.0ms	(.f64 (.f64 x x) 9/40)

Compiler

Compiled 222 to 201 computations (9.5% saved)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4875	881
1	4875	881

prune123.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	73	5	78

Error

Counts

78 → 5

Compiler

Compiled 1249 to 900 computations (27.9% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.4b	(-.f64 x (sin.f64 x))
1.4b	(-.f64 x (tan.f64 x))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite105.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
202×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip--_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 232

Calls

8 calls:

23.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
15.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
7.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))
0.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

series496.0ms (2.6%)

Counts

4 → 35

Calls

4 calls:

188.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
160.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
100.0ms	(-.f64 x (tan.f64 x))
47.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 838 to 607 computations (27.6% saved)

simplify191.0ms (1%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5220	6820

prune340.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	267	5	272

Error

Counts

272 → 5

Compiler

Compiled 5434 to 1267 computations (76.7% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	250	547
1	250	547

regimes232.0ms (1.2%)

Accuracy

Total 0.0b remaining (42.6%)

Threshold costs 0.0b (42.6%)

Compiler

Compiled 800 to 507 computations (36.6% saved)

bsearch75.0ms (0.4%)

Steps

Iters	Range		Point
9	0.0010744360172732811	35565.604513210026	0.02979588450427104
8	-42.302475981826355	-0.0033328734563595743	-0.025909900776185827

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	78
1	101	78

end0.0ms (0%)

sample12.9s (67.6%)

Algorithm

1×

intervals

Results

6.9s	1944×	body	2048	valid
1.8s	2997×	body	1024	valid
490.0ms	1516×	body	512	valid
219.0ms	119×	body	4096	valid
176.0ms	788×	body	256	valid
81.0ms	636×	body	128	valid

Compiler

Compiled 1168 to 738 computations (36.8% saved)

Pareto

-0.24596784698186983

Details

analyze2.2s (11.6%)

sample394.0ms (2.1%)

simplify316.0ms (1.7%)

prune7.0ms (0%)

localize17.0ms (0.1%)

rewrite62.0ms (0.3%)

series384.0ms (2%)

simplify79.0ms (0.4%)

prune239.0ms (1.3%)

localize17.0ms (0.1%)

rewrite48.0ms (0.3%)

series174.0ms (0.9%)

simplify109.0ms (0.6%)

prune130.0ms (0.7%)

localize16.0ms (0.1%)

rewrite44.0ms (0.2%)

series172.0ms (0.9%)

simplify142.0ms (0.7%)

prune123.0ms (0.6%)

localize17.0ms (0.1%)

rewrite105.0ms (0.5%)

series496.0ms (2.6%)

simplify191.0ms (1%)

prune340.0ms (1.8%)

simplify20.0ms (0.1%)

regimes232.0ms (1.2%)

bsearch75.0ms (0.4%)

simplify5.0ms (0%)

end0.0ms (0%)

sample12.9s (67.6%)

Profiling