Details

analyze1.3s (13.5%)

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)

sample160.0ms (1.6%)

Algorithm

1×

intervals

Results

92.0ms	60×	body	2048	valid
34.0ms	94×	body	1024	valid
9.0ms	44×	body	512	valid
8.0ms	30×	body	256	valid
6.0ms	5×	body	4096	valid
2.0ms	23×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify231.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

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: 27.8b

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)))
1.6b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 x (sin.f64 x))

rewrite26.0ms (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))
3.0ms	(-.f64 x (tan.f64 x))

series280.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

127.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
99.0ms	(-.f64 x (tan.f64 x))
54.0ms	(-.f64 x (sin.f64 x))

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4845	1797
1	4845	1797

prune78.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

Compiler

Compiled 1573 to 328 computations (79.1% saved)

localize12.0ms (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))))
1.6b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 x (tan.f64 x))

rewrite54.0ms (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:

31.0ms	(-.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))

series518.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
92.0ms	(-.f64 x (tan.f64 x))
90.0ms	(-.f64 x (tan.f64 x))
89.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5147	2253

prune84.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	103	4	107

Merged error: 0.0b

Counts

107 → 4

Compiler

Compiled 2363 to 457 computations (80.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 x (sin.f64 x))
1.6b	(-.f64 x (sin.f64 x))
1.6b	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series230.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(-.f64 x (tan.f64 x))
52.0ms	(-.f64 x (sin.f64 x))
44.0ms	(-.f64 x (sin.f64 x))
43.0ms	(-.f64 x (sin.f64 x))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5011	778

prune72.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	64	4	68

Merged error: 0.0b

Counts

68 → 4

Compiler

Compiled 2422 to 350 computations (85.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
17.1b	(-.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

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:

8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 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))

series143.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

55.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
53.0ms	(*.f64 27/2800 (pow.f64 x 4))
34.0ms	(.f64 (.f64 x x) 9/40)

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4833	850
1	4833	850

prune65.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 1144 to 836 computations (26.9% saved)

regimes40.0ms (0.4%)

Compiler: Compiled 176 to 88 computations (50% saved)

bsearch50.0ms (0.5%)

Steps

Iters	Range		Point
9	3.558971160277299e-06	1.8429315926685144	0.03373148106887707
10	-64081696.566474	-0.0004604258194533196	-0.03034462930623491

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	96	55
1	96	55

end0.0ms (0%)

sample6.2s (62.1%)

Algorithm

1×

intervals

Results

4.0s	1996×	body	2048	valid
1.2s	2979×	body	1024	valid
321.0ms	1543×	body	512	valid
149.0ms	111×	body	4096	valid
101.0ms	760×	body	256	valid
49.0ms	611×	body	128	valid

Compiler

Compiled 124 to 69 computations (44.4% saved)

Details

analyze1.3s (13.5%)

sample160.0ms (1.6%)

simplify231.0ms (2.3%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite26.0ms (0.3%)

series280.0ms (2.8%)

simplify100.0ms (1%)

prune78.0ms (0.8%)

localize12.0ms (0.1%)

rewrite54.0ms (0.5%)

series518.0ms (5.2%)

simplify74.0ms (0.7%)

prune84.0ms (0.8%)

localize13.0ms (0.1%)

rewrite22.0ms (0.2%)

series230.0ms (2.3%)

simplify73.0ms (0.7%)

prune72.0ms (0.7%)

localize9.0ms (0.1%)

rewrite24.0ms (0.2%)

series143.0ms (1.4%)

simplify36.0ms (0.4%)

prune65.0ms (0.7%)

regimes40.0ms (0.4%)

bsearch50.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.2s (62.1%)

Profiling