Details

analyze1.2s (12.2%)

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)

sample218.0ms (2.3%)

Algorithm

1×

intervals

Results

122.0ms	46×	body	2560	valid
60.0ms	93×	body	1280	valid
19.0ms	68×	body	640	valid
5.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	9×	body	80	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify528.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	1006	14
1	1006	14

prune5.0ms (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: 32.5b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_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 → 78

Calls

3 calls:

26.0ms	(/.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))

series38.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(-.f64 x (sin.f64 x))
12.0ms	(-.f64 x (tan.f64 x))
12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

simplify111.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4866	1817
1	4866	1817

prune50.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	2	88

Merged error: 0b

Counts

88 → 2

Compiler

Compiled 1536 to 328 computations (78.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
14.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_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`
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 → 57

Calls

3 calls:

10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
8.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)

series13.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))
4.0ms	(*.f64 27/2800 (pow.f64 x 4))
3.0ms	(.f64 (.f64 x x) 9/40)

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4963	856
1	4963	856

prune49.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Merged error: 0b

Counts

68 → 2

Compiler

Compiled 1158 to 843 computations (27.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
1.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (tan.f64 x))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

29.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series53.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
11.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
9.0ms	(-.f64 x (tan.f64 x))
9.0ms	(-.f64 x (tan.f64 x))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5030	2287

prune45.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	103	2	105

Merged error: 0b

Counts

105 → 2

Compiler

Compiled 2322 to 446 computations (80.8% saved)

regimes23.0ms (0.2%)

Compiler: Compiled 29 to 20 computations (31% saved)

bsearch41.0ms (0.4%)

Steps

Iters	Range		Point
10	7.560806448836807e-16	106.74986232706004	0.0297212302942771
10	-130721547920.48747	-9.057675229687969e-07	-0.03513683975429144

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	96	55
1	96	55

end0.0ms (0%)

sample6.9s (72.5%)

Algorithm

1×

intervals

Results

4.2s	1665×	body	2560	valid
1.6s	2782×	body	1280	valid
494.0ms	1838×	body	640	valid
158.0ms	879×	body	320	valid
57.0ms	439×	body	160	valid
33.0ms	397×	body	80	valid

Compiler

Compiled 73 to 50 computations (31.5% saved)

Details

analyze1.2s (12.2%)

sample218.0ms (2.3%)

simplify528.0ms (5.5%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite40.0ms (0.4%)

series38.0ms (0.4%)

simplify111.0ms (1.2%)

prune50.0ms (0.5%)

localize8.0ms (0.1%)

rewrite25.0ms (0.3%)

series13.0ms (0.1%)

simplify47.0ms (0.5%)

prune49.0ms (0.5%)

localize9.0ms (0.1%)

rewrite47.0ms (0.5%)

series53.0ms (0.6%)

simplify90.0ms (0.9%)

prune45.0ms (0.5%)

regimes23.0ms (0.2%)

bsearch41.0ms (0.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample6.9s (72.5%)

Profiling