Details

analyze1.5s (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample103.0ms (0.7%)

Algorithm

1×

intervals

Results

41.0ms	64×	body	1024	valid
17.0ms	131×	body	128	valid
15.0ms	39×	body	512	valid
6.0ms	22×	body	256	valid
4.0ms	30×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify231.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune11.0ms (0.1%)

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

10.5b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize26.0ms (0.2%)

Local error

Found 8 expressions with local error:

4.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
4.6b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

8 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))
0.0ms	(-.f64 (.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2)) (/.f64 x (tan.f64 B)))

series981.0ms (6.4%)

Counts

4 → 51

Calls

4 calls:

423.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
249.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
207.0ms	(/.f64 x (tan.f64 B))
101.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 2663 to 2144 computations (19.5% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5183	3735

prune377.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	155	11	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	11	168

Error

0.0b

Counts

168 → 11

Compiler

Compiled 4980 to 2469 computations (50.4% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.1b	(/.f64 x (tan.f64 B))
0.0b	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

8 calls:

12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))
0.0ms	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))

series1.0s (6.8%)

Counts

4 → 55

Calls

4 calls:

414.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
235.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
198.0ms	(/.f64 x (tan.f64 B))
195.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

Compiler

Compiled 2963 to 2412 computations (18.6% saved)

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4936	3592
1	4936	3592

prune222.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	149	10	159

Error

0.0b

Counts

159 → 10

Compiler

Compiled 4404 to 2413 computations (45.2% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.2b	(/.f64 (tan.f64 B) x)
0.0b	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
11×	`div-exp_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`pow1_binary64` `prod-exp_binary64` `div-inv_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 141

Calls

8 calls:

12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
11.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
0.0ms	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))

series1.0s (6.7%)

Counts

4 → 55

Calls

4 calls:

401.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
226.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
198.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
193.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

Compiler

Compiled 3089 to 2538 computations (17.8% saved)

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4919	4463
1	4919	4463

prune312.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Error

0.0b

Counts

206 → 8

Compiler

Compiled 6048 to 3292 computations (45.6% saved)

localize34.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.1b	(/.f64 1 (tan.f64 B))
0.0b	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite95.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

446×	`times-frac_binary64`
219×	`add-sqr-sqrt_binary64`
214×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
60×	`add-exp-log_binary64`
36×	`div-exp_binary64`
31×	`div-inv_binary64`
23×	`add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
15×	`associate-/r/_binary64` `associate-/l*_binary64`
14×	`tan-quot_binary64`
10×	`cbrt-undiv_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`prod-exp_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `pow-pow_binary64` `*-commutative_binary64`

Counts

4 → 306

Calls

8 calls:

14.0ms	(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
0.0ms	(-.f64 (/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))

series1.0s (6.7%)

Counts

4 → 55

Calls

4 calls:

410.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
225.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
198.0ms	(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
190.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

Compiler

Compiled 3215 to 2664 computations (17.1% saved)

simplify127.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

361 → 361

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4942	8810
1	4942	8810

prune737.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	361	0	361
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	361	8	369

Error

0.0b

Counts

369 → 8

Compiler

Compiled 11802 to 6684 computations (43.4% saved)

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	854	2981
1	854	2981

regimes550.0ms (3.6%)

Compiler: Compiled 5703 to 4398 computations (22.9% saved)

bsearch120.0ms (0.8%)

Steps

Iters	Range		Point
8	46318825.02109967	497725499837.33624	94181933.04629011
7	-7.570107378107944e+84	-4.1945670733272555e+83	-7.377918106249466e+84

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes138.0ms (0.9%)

Compiler: Compiled 978 to 885 computations (9.5% saved)

bsearch135.0ms (0.9%)

Steps

Iters	Range		Point
8	46318825.02109967	497725499837.33624	122347326.68899404
9	-1.0799752384234898e+74	-2.766334003256559e+68	-1.74275693971342e+71

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes137.0ms (0.9%)

Compiler: Compiled 756 to 690 computations (8.7% saved)

bsearch119.0ms (0.8%)

Steps

Iters	Range		Point
8	46318825.02109967	497725499837.33624	473578177.1459986
7	-7.570107378107944e+84	-4.1945670733272555e+83	-1.8011926095838173e+84

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes235.0ms (1.5%)

Compiler: Compiled 702 to 645 computations (8.1% saved)

bsearch222.0ms (1.5%)

Steps

Iters	Range		Point
11	2.7347844038859524e-38	1.480431128182521e-14	1.4530646468251453e-14
9	1.173785904910786e-114	8.805970253882878e-109	7.764958837944096e-109
7	-0.03289737887528019	-0.0008188160127484041	-0.03224115561723573

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes167.0ms (1.1%)

Compiler: Compiled 435 to 426 computations (2.1% saved)

bsearch175.0ms (1.2%)

Steps

Iters	Range		Point
11	2.7347844038859524e-38	1.480431128182521e-14	1.2181432083136693e-14
10	-0.0008188160127484041	-2.6458753263560236e-16	-0.0008089251371989151

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes109.0ms (0.7%)

Compiler: Compiled 315 to 330 computations (-4.8% saved)

bsearch63.0ms (0.4%)

Steps

Iters	Range		Point
8	-1.31241874281642e-300	-2.6349693895878495e-303	-4.225797020350178e-301

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.2%)

Compiler: Compiled 42 to 81 computations (-92.9% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

Accuracy

Total 0.2b remaining (90%)

Threshold costs 0.2b (90%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch13.0ms (0.1%)

Compiler: Compiled 283 to 184 computations (35% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	115	433
1	115	433

end0.0ms (0%)

sample4.6s (30.3%)

Algorithm

1×

intervals

Results

1.2s	2135×	body	1024	valid
533.0ms	4153×	body	128	valid
436.0ms	1142×	body	512	valid
139.0ms	564×	body	256	valid
86.0ms	700×	body	128	invalid
13.0ms	131×	body	128	nan
6.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 2210 to 1671 computations (24.4% saved)

Pareto

-0.009597943369560193

Details

analyze1.5s (10%)

sample103.0ms (0.7%)

simplify231.0ms (1.5%)

prune11.0ms (0.1%)

localize26.0ms (0.2%)

rewrite45.0ms (0.3%)

series981.0ms (6.4%)

simplify69.0ms (0.5%)

prune377.0ms (2.5%)

localize18.0ms (0.1%)

rewrite45.0ms (0.3%)

series1.0s (6.8%)

simplify101.0ms (0.7%)

prune222.0ms (1.5%)

localize21.0ms (0.1%)

rewrite53.0ms (0.3%)

series1.0s (6.7%)

simplify111.0ms (0.7%)

prune312.0ms (2%)

localize34.0ms (0.2%)

rewrite95.0ms (0.6%)

series1.0s (6.7%)

simplify127.0ms (0.8%)

prune737.0ms (4.8%)

simplify45.0ms (0.3%)

regimes550.0ms (3.6%)

bsearch120.0ms (0.8%)

regimes138.0ms (0.9%)

bsearch135.0ms (0.9%)

regimes137.0ms (0.9%)

bsearch119.0ms (0.8%)

regimes235.0ms (1.5%)

bsearch222.0ms (1.5%)

regimes167.0ms (1.1%)

bsearch175.0ms (1.2%)

regimes109.0ms (0.7%)

bsearch63.0ms (0.4%)

regimes30.0ms (0.2%)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

bsearch13.0ms (0.1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample4.6s (30.3%)

Profiling