Details

analyze9.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample45.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify409.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	5023	37

prune12.0ms (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

1.3b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
9.4b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
9.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite506.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_2124`
34×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `distribute-lft-out_binary64_2075`
24×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
21×	`add-sqr-sqrt_binary64_2146` `associate-r_binary64_2064`
18×	`associate-/r/_binary64_2070`
16×	`frac-times_binary64_2134`
15×	`add-cube-cbrt_binary64_2159`
14×	`times-frac_binary64_2130`
13×	`pow1_binary64_2185`
11×	`swap-sqr_binary64_2091`
10×	`prod-exp_binary64_2173` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `cbrt-unprod_binary64_2157` `associate-*l/_binary64_2067`
9×	`associate-l_binary64_2065`
8×	`associate-*r/_binary64_2066`
7×	`associate-/l/_binary64_2071`
6×	`associate-/r*_binary64_2068`
5×	`associate-/l*_binary64_2069`
4×	`add-log-exp_binary64_2163`
3×	`div-inv_binary64_2121` `unswap-sqr_binary64_2092`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `pow-prod-down_binary64_2195` `*-commutative_binary64_2055`
1×	`pow2_binary64_2205` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 158

Calls

4 calls:

27.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
23.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
23.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series3.3s (6.2%)

Error

0.2b

Counts

4 → 90

Calls

4 calls:

1.3s	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
670.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
471.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
128.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 17370 to 13805 computations (20.5% saved)

simplify152.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5082	15117

prune1.2s (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	238	10	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	240	10	250

Error

0.0b

Counts

250 → 10

Compiler

Compiled 13448 to 9095 computations (32.4% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
9.4b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))

rewrite1.8s (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

826×	`*-un-lft-identity_binary64_2124`
508×	`times-frac_binary64_2130`
374×	`distribute-lft-out_binary64_2075`
191×	`add-sqr-sqrt_binary64_2146`
182×	`add-cube-cbrt_binary64_2159`
136×	`associate-r_binary64_2064`
34×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
31×	`associate-/l*_binary64_2069`
30×	`associate-/r/_binary64_2070`
20×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
15×	`div-inv_binary64_2121` `associate-/r*_binary64_2068`
14×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
8×	`associate-/l/_binary64_2071`
6×	`pow1_binary64_2185` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-l*_binary64_2065`
3×	`unswap-sqr_binary64_2092` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
2×	`associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `*-commutative_binary64_2055`

Counts

4 → 422

Calls

4 calls:

68.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
62.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
27.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 16960 to 11567 computations (31.8% saved)

series3.3s (6.4%)

Error

0.0b

Counts

4 → 96

Calls

4 calls:

1.4s	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
612.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
460.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
207.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 18836 to 14883 computations (21% saved)

simplify246.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5002	24876

prune2.4s (4.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	516	2	518
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	518	10	528

Error

Counts

528 → 10

Compiler

Compiled 24456 to 16833 computations (31.2% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
9.4b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))

rewrite1.9s (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

829×	`*-un-lft-identity_binary64_2124`
394×	`times-frac_binary64_2130`
355×	`distribute-lft-out_binary64_2075`
248×	`sqrt-prod_binary64_2140`
224×	`add-sqr-sqrt_binary64_2146`
149×	`add-cube-cbrt_binary64_2159`
127×	`swap-sqr_binary64_2091`
45×	`associate-l_binary64_2065`
42×	`associate-r_binary64_2064`
38×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
16×	`pow1_binary64_2185`
14×	`associate-/l*_binary64_2069`
13×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
12×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/r/_binary64_2070`
10×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-times_binary64_2134` `unswap-sqr_binary64_2092` `associate-/r*_binary64_2068`
7×	`associate-*r/_binary64_2066`
6×	`associate-*l/_binary64_2067` `div-inv_binary64_2121`
4×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `sqrt-div_binary64_2141` `associate-/l/_binary64_2071`
2×	`*-commutative_binary64_2055` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`pow2_binary64_2205` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097`

Counts

4 → 405

Calls

4 calls:

66.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
33.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
11.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 18570 to 13888 computations (25.2% saved)

series2.0s (3.8%)

Error

Counts

4 → 84

Calls

4 calls:

680.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
469.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta))))
213.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
199.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 13612 to 10715 computations (21.3% saved)

simplify213.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

489 → 489

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5055	20609

prune2.2s (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	489	10	499

Error

Counts

499 → 10

Compiler

Compiled 21996 to 15741 computations (28.4% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

9.4b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
9.4b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
17.7b	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
17.7b	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))

rewrite2.7s (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

738×	`*-un-lft-identity_binary64_2124`
476×	`times-frac_binary64_2130`
334×	`distribute-lft-out_binary64_2075`
272×	`associate-r_binary64_2064`
184×	`add-sqr-sqrt_binary64_2146`
164×	`add-cube-cbrt_binary64_2159`
28×	`associate-/r/_binary64_2070`
22×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `sqrt-prod_binary64_2140`
18×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
14×	`div-inv_binary64_2121`
10×	`pow1_binary64_2185`
8×	`associate-l_binary64_2065`
6×	`div-exp_binary64_2175` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092`
4×	`add-log-exp_binary64_2163` `frac-times_binary64_2134` `associate-*l/_binary64_2067`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `associate-r/_binary64_2066` `-commutative_binary64_2055`

Counts

4 → 370

Calls

4 calls:

71.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
70.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
37.0ms	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
36.0ms	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))

Compiler

Compiled 25668 to 18419 computations (28.2% saved)

series15.0s (28.9%)

Error

Counts

4 → 96

Calls

4 calls:

5.1s	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
4.9s	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
711.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
698.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))

Compiler

Compiled 57512 to 46101 computations (19.8% saved)

simplify384.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

466 → 466

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5034	49976

prune7.2s (13.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	466	0	466
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	466	10	476

Error

Counts

476 → 10

Compiler

Compiled 53324 to 38733 computations (27.4% saved)

regimes1.5s (2.8%)

Accuracy

Total 0.1b remaining (94.6%)

Threshold costs 0.1b (94.6%)

Compiler

Compiled 16454 to 12197 computations (25.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	37
1	28	37

end0.0ms (0%)

sample5.6s (10.8%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
159.0ms	8000×	pre	128	true

Compiler

Compiled 5527 to 4097 computations (25.9% saved)

Details

analyze9.0ms (0%)

sample45.0ms (0.1%)

simplify409.0ms (0.8%)

prune12.0ms (0%)

localize16.0ms (0%)

rewrite506.0ms (1%)

series3.3s (6.2%)

simplify152.0ms (0.3%)

prune1.2s (2.2%)

localize17.0ms (0%)

rewrite1.8s (3.5%)

series3.3s (6.4%)

simplify246.0ms (0.5%)

prune2.4s (4.5%)

localize24.0ms (0%)

rewrite1.9s (3.7%)

series2.0s (3.8%)

simplify213.0ms (0.4%)

prune2.2s (4.2%)

localize24.0ms (0%)

rewrite2.7s (5.2%)

series15.0s (28.9%)

simplify384.0ms (0.7%)

prune7.2s (13.8%)

regimes1.5s (2.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.6s (10.8%)

Profiling