Details

analyze14.1s (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
6.2%	93.5%	0.2%	11
6.2%	93.5%	0.2%	12
7.8%	92%	0.2%	13
8.6%	91.2%	0.2%	14

Compiler

Compiled 110 to 84 computations (23.6% saved)

sample1.7s (2.1%)

Algorithm

1×

intervals

Results

568.0ms	58×	body	4096	valid
304.0ms	48×	body	2048	invalid
272.0ms	47×	body	2048	valid
136.0ms	16×	body	4096	invalid
131.0ms	33×	body	1024	valid
78.0ms	101×	body	128	valid
67.0ms	3×	body	8192	invalid
57.0ms	16×	body	1024	invalid
29.0ms	2×	body	8192	valid
23.0ms	8×	body	512	valid
13.0ms	18×	body	128	invalid
11.0ms	6×	body	512	invalid
10.0ms	7×	body	256	valid
4.0ms	3×	body	256	invalid

Compiler

Compiled 219 to 172 computations (21.5% saved)

simplify182.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5232	172

prune13.0ms (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

44.1b

Counts

2 → 2

Compiler

Compiled 323 to 229 computations (29.1% saved)

localize91.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.6b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
32.4b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))

rewrite76.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-*r/_binary64_361`
9×	`frac-sub_binary64_428`
7×	`associate-*l/_binary64_362`
6×	`add-log-exp_binary64_458` `frac-times_binary64_429`
4×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
2×	`sub-div_binary64_426`
1×	`sub-neg_binary64_412` `flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 44

Calls

4 calls:

50.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

series2.2s (2.7%)

Counts

4 → 12

Calls

4 calls:

2.1s	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2)) y-scale) y-scale)))
22.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
21.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
21.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

simplify128.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5054	5163

prune587.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	51	7	58

Error

36.3b

Counts

58 → 7

Compiler

Compiled 7356 to 4950 computations (32.7% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.0b	(.f64 x-scale (.f64 y-scale y-scale))
18.7b	(.f64 (.f64 b b) (*.f64 a a))
20.2b	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite74.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
79×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
46×	`pow1_binary64_480`
23×	`pow-prod-down_binary64_490`
20×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
7×	`add-sqr-sqrt_binary64_441` `associate-l_binary64_360`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`add-log-exp_binary64_458` `pow-plus_binary64_482` `pow-prod-up_binary64_489`
3×	`associate-r_binary64_359` `*-commutative_binary64_350`
2×	`unswap-sqr_binary64_387` `pow-sqr_binary64_392` `pow2_binary64_500`
1×	`clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 122

Calls

4 calls:

25.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
10.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
6.0ms	(.f64 x-scale (.f64 y-scale y-scale))

series225.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
33.0ms	(.f64 x-scale (.f64 y-scale y-scale))
31.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
27.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify114.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4996	1898
1	4996	1898

prune266.0ms (0.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	127	14	141

Error

18.0b

Counts

141 → 14

Compiler

Compiled 3143 to 1457 computations (53.6% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 b a) 2)
3.7b	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
8.0b	(.f64 x-scale (.f64 y-scale y-scale))
20.2b	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))

rewrite59.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_457`
38×	`prod-exp_binary64_468`
32×	`add-cbrt-cube_binary64_455`
21×	`pow1_binary64_480`
16×	`div-exp_binary64_470`
15×	`cbrt-unprod_binary64_452`
10×	`pow-prod-down_binary64_490` `add-sqr-sqrt_binary64_441` `pow-exp_binary64_487`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `associate-l_binary64_360` `associate-/l*_binary64_364`
5×	`pow-to-exp_binary64_488`
4×	`add-log-exp_binary64_458` `cbrt-undiv_binary64_453`
3×	`unpow-prod-down_binary64_498` `sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`associate-r_binary64_359` `*-commutative_binary64_350` `pow-pow_binary64_491`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `associate-/r*_binary64_363`

Counts

4 → 101

Calls

4 calls:

21.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
15.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
11.0ms	(.f64 x-scale (.f64 y-scale y-scale))
4.0ms	(pow.f64 (*.f64 b a) 2)

series206.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(/.f64 (pow.f64 (.f64 b a) 2) (.f64 x-scale (.f64 x-scale (.f64 y-scale y-scale))))
42.0ms	(pow.f64 (*.f64 b a) 2)
36.0ms	(.f64 x-scale (.f64 x-scale (*.f64 y-scale y-scale)))
32.0ms	(.f64 x-scale (.f64 y-scale y-scale))

simplify134.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4998	1469
1	4998	1469

prune166.0ms (0.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	10	2	12
Picked	1	0	1
Done	1	0	1
Total	116	11	127

Error

0.7b

Counts

127 → 11

Compiler

Compiled 2245 to 1049 computations (53.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
0.2b	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
8.9b	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
8.9b	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64_441`
44×	`times-frac_binary64_425`
37×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
35×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
32×	`associate-l_binary64_360`
30×	`associate-r_binary64_359`
20×	`pow1_binary64_480`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`unswap-sqr_binary64_387`
8×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416` `*-commutative_binary64_350`
3×	`swap-sqr_binary64_386`
2×	`associate-l/_binary64_362` `frac-times_binary64_429` `associate-r/_binary64_361`
1×	`sqr-abs_binary64_434` `pow-plus_binary64_482` `pow-sqr_binary64_392` `pow-prod-up_binary64_489` `pow2_binary64_500`

Counts

4 → 145

Calls

4 calls:

11.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
11.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
6.0ms	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
4.0ms	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))

series158.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 -4 (.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale)))))
40.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))
36.0ms	(.f64 (fabs.f64 (.f64 (/.f64 a x-scale) (/.f64 b y-scale))) (fabs.f64 (*.f64 (/.f64 a x-scale) (/.f64 b y-scale))))
31.0ms	(*.f64 (/.f64 a x-scale) (/.f64 b y-scale))

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5070	2268

prune204.0ms (0.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	146	11	157
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	149	19	168

Error

0.5b

Counts

168 → 19

Compiler

Compiled 3504 to 826 computations (76.4% saved)

regimes2.9s (3.5%)

Accuracy

Total 5.3b remaining (87.2%)

Threshold costs 0b (0%)

Compiler

Compiled 31372 to 22664 computations (27.8% saved)

bsearch1.7s (2.1%)

Steps

Iters	Range		Point
7	6.7431010476414834e+78	4.5777519943782413e+80	2.598555315437982e+79
6	9.985216439922526e-118	5.0472544513842396e-117	3.833516390112431e-117

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	91
1	37	91

end0.0ms (0%)

sample56.7s (68.9%)

Algorithm

1×

intervals

Results

13.9s	1441×	body	4096	valid
9.9s	1629×	body	2048	valid
7.7s	804×	body	4096	invalid
6.8s	1177×	body	2048	invalid
3.5s	918×	body	1024	valid
2.8s	3446×	body	128	valid
2.5s	670×	body	1024	invalid
1.1s	52×	body	8192	valid
906.0ms	42×	body	8192	invalid
893.0ms	383×	body	512	valid
683.0ms	1019×	body	128	invalid
671.0ms	285×	body	512	invalid
173.0ms	131×	body	256	valid
172.0ms	110×	body	256	invalid

Compiler

Compiled 4062 to 2920 computations (28.1% saved)

Details

analyze14.1s (17.2%)

sample1.7s (2.1%)

simplify182.0ms (0.2%)

prune13.0ms (0%)

localize91.0ms (0.1%)

rewrite76.0ms (0.1%)

series2.2s (2.7%)

simplify128.0ms (0.2%)

prune587.0ms (0.7%)

localize23.0ms (0%)

rewrite74.0ms (0.1%)

series225.0ms (0.3%)

simplify114.0ms (0.1%)

prune266.0ms (0.3%)

localize22.0ms (0%)

rewrite59.0ms (0.1%)

series206.0ms (0.3%)

simplify134.0ms (0.2%)

prune166.0ms (0.2%)

localize9.0ms (0%)

rewrite44.0ms (0.1%)

series158.0ms (0.2%)

simplify93.0ms (0.1%)

prune204.0ms (0.2%)

regimes2.9s (3.5%)

bsearch1.7s (2.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample56.7s (68.9%)

Profiling