Details

analyze46.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample37.0ms (0.1%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5395	79

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

53.5b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 i (+.f64 (+.f64 alpha beta) i))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
38.0b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
45.5b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite147.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_1789`
66×	`associate-/r/_binary64_1729`
61×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `flip-+_binary64_1757` `flip3-+_binary64_1786`
47×	`*-un-lft-identity_binary64_1783`
44×	`add-sqr-sqrt_binary64_1805`
40×	`frac-times_binary64_1793`
34×	`associate-*r/_binary64_1725`
28×	`difference-of-squares_binary64_1752` `add-cube-cbrt_binary64_1818`
22×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
20×	`associate-*l/_binary64_1726`
19×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
14×	`associate-/l*_binary64_1728` `difference-of-sqr-1_binary64_1753`
11×	`pow1_binary64_1844`
9×	`associate-/l/_binary64_1730` `div-inv_binary64_1780`
8×	`associate-r_binary64_1723`
7×	`associate-/r*_binary64_1727`
4×	`associate-l_binary64_1724` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
3×	`distribute-lft-out_binary64_1734`
2×	`distribute-lft-in_binary64_1732` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `unswap-sqr_binary64_1751` `flip--_binary64_1758`

Counts

4 → 217

Calls

4 calls:

45.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
27.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
9.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

series12.5s (35.8%)

Counts

4 → 98

Calls

4 calls:

10.8s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
1.1s	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
485.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
126.0ms	(*.f64 i (+.f64 (+.f64 alpha beta) i))

Compiler

Compiled 21198 to 15138 computations (28.6% saved)

simplify250.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	28207
1	4961	28207

prune1.4s (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	306	9	315
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	9	316

Error

8.6b

Counts

316 → 9

Compiler

Compiled 26225 to 11507 computations (56.1% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune20.0ms (0.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

8.6b

Counts

9 → 9

Compiler

Compiled 495 to 298 computations (39.8% saved)

localize88.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.5b	(/.f64 (*.f64 alpha alpha) (/.f64 (pow.f64 i 3) beta))
14.2b	(/.f64 (*.f64 beta (pow.f64 alpha 3)) (pow.f64 i 4))
15.0b	(/.f64 (pow.f64 alpha 3) (pow.f64 i 3))
15.9b	(/.f64 (pow.f64 alpha 4) (pow.f64 i 4))

rewrite360.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

312×	`times-frac_binary64_1789`
162×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
150×	`unpow-prod-down_binary64_1862`
96×	`cube-prod_binary64_1811`
78×	`add-exp-log_binary64_1821`
66×	`associate-/r*_binary64_1727`
50×	`sqr-pow_binary64_1755`
44×	`div-exp_binary64_1834`
32×	`cube-mult_binary64_1813` `unpow3_binary64_1849`
25×	`add-cbrt-cube_binary64_1819`
21×	`associate-/l*_binary64_1728` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
13×	`prod-exp_binary64_1832`
10×	`cbrt-undiv_binary64_1817`
6×	`div-inv_binary64_1780`
4×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `add-log-exp_binary64_1822` `pow1_binary64_1844`
3×	`cbrt-unprod_binary64_1816`
1×	`associate-/r/_binary64_1729`

Counts

4 → 414

Calls

4 calls:

12.0ms	(/.f64 (*.f64 alpha alpha) (/.f64 (pow.f64 i 3) beta))
11.0ms	(/.f64 (pow.f64 alpha 3) (pow.f64 i 3))
7.0ms	(/.f64 (*.f64 beta (pow.f64 alpha 3)) (pow.f64 i 4))
7.0ms	(/.f64 (pow.f64 alpha 4) (pow.f64 i 4))

series974.0ms (2.8%)

Counts

4 → 30

Calls

4 calls:

315.0ms	(/.f64 (*.f64 beta (pow.f64 alpha 3)) (pow.f64 i 4))
289.0ms	(/.f64 (*.f64 alpha alpha) (/.f64 (pow.f64 i 3) beta))
186.0ms	(/.f64 (pow.f64 alpha 4) (pow.f64 i 4))
182.0ms	(/.f64 (pow.f64 alpha 3) (pow.f64 i 3))

Compiler

Compiled 10380 to 7056 computations (32% saved)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

444 → 444

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4987	7241
1	4987	7241

prune8.5s (24.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	444	0	444
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	444	9	453

Error

8.6b

Counts

453 → 9

Compiler

Compiled 79526 to 47414 computations (40.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
34.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
34.7b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

rewrite130.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1789`
174×	`*-un-lft-identity_binary64_1783`
170×	`add-sqr-sqrt_binary64_1805`
106×	`add-cube-cbrt_binary64_1818`
34×	`associate-/r/_binary64_1729`
32×	`difference-of-squares_binary64_1752`
28×	`associate-/l*_binary64_1728`
25×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
18×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
17×	`div-inv_binary64_1780` `associate-/r*_binary64_1727`
16×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
11×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
10×	`distribute-lft-out_binary64_1734`
6×	`associate-/l/_binary64_1730`
4×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
1×	`flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 268

Calls

4 calls:

22.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
22.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
13.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series4.6s (13.2%)

Counts

4 → 107

Calls

4 calls:

2.8s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
1.1s	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
380.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
282.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 16678 to 11497 computations (31.1% saved)

simplify237.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4983	28849
1	4983	28849

prune1.7s (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	372	3	375
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	375	9	384

Error

8.6b

Counts

384 → 9

Compiler

Compiled 32014 to 14172 computations (55.7% saved)

regimes861.0ms (2.5%)

Accuracy

Total 3.0b remaining (28.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15248 to 8285 computations (45.7% saved)

bsearch21.0ms (0.1%)

Steps

Iters	Range		Point
4	2.0404324899732053e+141	3.804055376735248e+141	2.863302589093192e+141

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	92
1	45	92

end0.0ms (0%)

sample2.8s (8%)

Algorithm

1×

intervals

Results

652.0ms	8000×	body	128	valid
181.0ms	8000×	pre	128	true

Compiler

Compiled 3869 to 2104 computations (45.6% saved)

Details

analyze46.0ms (0.1%)

sample37.0ms (0.1%)

simplify133.0ms (0.4%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite147.0ms (0.4%)

series12.5s (35.8%)

simplify250.0ms (0.7%)

prune1.4s (4%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune20.0ms (0.1%)

localize88.0ms (0.3%)

rewrite360.0ms (1%)

series974.0ms (2.8%)

simplify128.0ms (0.4%)

prune8.5s (24.3%)

localize19.0ms (0.1%)

rewrite130.0ms (0.4%)

series4.6s (13.2%)

simplify237.0ms (0.7%)

prune1.7s (4.8%)

regimes861.0ms (2.5%)

bsearch21.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.8s (8%)

Profiling