Details

analyze1.4s (13.7%)

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)

sample188.0ms (1.9%)

Algorithm

1×

intervals

Results

121.0ms	69×	body	2048	valid
38.0ms	90×	body	1024	valid
10.0ms	51×	body	512	valid
4.0ms	3×	body	4096	valid
3.0ms	21×	body	256	valid
2.0ms	22×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify235.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	990	14
1	990	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

Merged error: 30.6b

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))

rewrite27.0ms (0.3%)

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:

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))

series288.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

114.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
113.0ms	(-.f64 x (tan.f64 x))
61.0ms	(-.f64 x (sin.f64 x))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4845	1797
1	4845	1797

prune81.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

Compiler

Compiled 1530 to 318 computations (79.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b	(log.f64 (exp.f64 (/.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))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
28×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 122

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series488.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
109.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
91.0ms	(-.f64 x (tan.f64 x))
49.0ms	(-.f64 x (sin.f64 x))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5617	2686

prune103.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

Compiler

Compiled 2640 to 546 computations (79.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x (tan.f64 x)))
0.1b	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`associate-/r_binary64` `associate-l*_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`unswap-sqr_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

16.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 1 (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series343.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(-.f64 x (tan.f64 x))
109.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
79.0ms	(/.f64 1 (-.f64 x (tan.f64 x)))
44.0ms	(-.f64 x (sin.f64 x))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5536	2157

prune96.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

Compiler

Compiled 2286 to 734 computations (67.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
14.3b	(-.f64 (+.f64 -1/2 (.f64 (.f64 x x) 9/40)) (*.f64 27/2800 (pow.f64 x 4)))

rewrite26.0ms (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` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

9.0ms	(.f64 (.f64 x x) 9/40)
7.0ms	(-.f64 (+.f64 -1/2 (.f64 (.f64 x x) 9/40)) (*.f64 27/2800 (pow.f64 x 4)))
6.0ms	(*.f64 27/2800 (pow.f64 x 4))

series152.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

58.0ms	(*.f64 27/2800 (pow.f64 x 4))
56.0ms	(-.f64 (+.f64 -1/2 (.f64 (.f64 x x) 9/40)) (*.f64 27/2800 (pow.f64 x 4)))
38.0ms	(.f64 (.f64 x x) 9/40)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5350	853

prune68.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

Compiler

Compiled 1144 to 828 computations (27.6% saved)

regimes40.0ms (0.4%)

Compiler: Compiled 120 to 94 computations (21.7% saved)

bsearch51.0ms (0.5%)

Steps

Iters	Range		Point
10	2.5055578474216267e-15	845.2894123143092	0.025115649644518994
8	-258.55589067087	-0.009869667097770632	-0.027966059282491268

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	51
1	74	51

end0.0ms (0%)

sample5.9s (59.7%)

Algorithm

1×

intervals

Results

3.8s	1981×	body	2048	valid
1.2s	3028×	body	1024	valid
316.0ms	1481×	body	512	valid
122.0ms	98×	body	4096	valid
103.0ms	761×	body	256	valid
58.0ms	651×	body	128	valid

Compiler

Compiled 93 to 73 computations (21.5% saved)

Details

analyze1.4s (13.7%)

sample188.0ms (1.9%)

simplify235.0ms (2.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite27.0ms (0.3%)

series288.0ms (2.9%)

simplify104.0ms (1.1%)

prune81.0ms (0.8%)

localize11.0ms (0.1%)

rewrite44.0ms (0.4%)

series488.0ms (4.9%)

simplify83.0ms (0.8%)

prune103.0ms (1%)

localize9.0ms (0.1%)

rewrite41.0ms (0.4%)

series343.0ms (3.5%)

simplify77.0ms (0.8%)

prune96.0ms (1%)

localize9.0ms (0.1%)

rewrite26.0ms (0.3%)

series152.0ms (1.5%)

simplify56.0ms (0.6%)

prune68.0ms (0.7%)

regimes40.0ms (0.4%)

bsearch51.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (59.7%)

Profiling