Details

analyze175.0ms (0.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5646	316
0	3	3
1	3	3

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

Symmetry

(sort alpha beta)

Compiler

Compiled 63 to 34 computations (46% saved)

sample49.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify42.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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

55.5b

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 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
37.9b	(/.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))
47.3b	(/.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))))

rewrite972.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

39.0b

Rules

86×	`times-frac_binary64_2130`
66×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/r/_binary64_2070`
61×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
46×	`add-sqr-sqrt_binary64_2146`
44×	`*-un-lft-identity_binary64_2124` `frac-times_binary64_2134`
34×	`associate-*r/_binary64_2066`
30×	`add-cube-cbrt_binary64_2159`
28×	`difference-of-squares_binary64_2093`
22×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-*l/_binary64_2067`
19×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
16×	`pow1_binary64_2185`
14×	`associate-/l*_binary64_2069` `difference-of-sqr-1_binary64_2094`
9×	`div-inv_binary64_2121` `associate-/l/_binary64_2071`
7×	`associate-/r*_binary64_2068`
6×	`associate-r_binary64_2064`
4×	`add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `associate-l_binary64_2065`
3×	`swap-sqr_binary64_2091`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `*-commutative_binary64_2055`
1×	`flip3--_binary64_2128` `flip--_binary64_2099` `pow2_binary64_2205` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097` `unswap-sqr_binary64_2092`

Counts

4 → 228

Calls

4 calls:

44.0ms	(/.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))
32.0ms	(/.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))))
14.0ms	(.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))))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series10.1s (21.9%)

Error

8.5b

Counts

4 → 86

Calls

4 calls:

8.4s	(/.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))
639.0ms	(/.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))))
437.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
233.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 24293 to 16280 computations (33% saved)

simplify205.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5717	24952

prune1.2s (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	306	8	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	8	315

Error

6.1b

Counts

315 → 8

Compiler

Compiled 24188 to 10702 computations (55.8% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 6.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune12.0ms (0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

6.1b

Counts

8 → 8

Compiler

Compiled 326 to 198 computations (39.3% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
35.6b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite2.7s (5.9%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

606×	`*-un-lft-identity_binary64_2124`
587×	`times-frac_binary64_2130`
379×	`add-sqr-sqrt_binary64_2146`
210×	`add-cube-cbrt_binary64_2159`
150×	`associate-r_binary64_2064`
129×	`distribute-lft-out_binary64_2075`
74×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
70×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
56×	`associate-l_binary64_2065`
54×	`associate-/r/_binary64_2070`
37×	`difference-of-sqr-1_binary64_2094`
33×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
27×	`div-inv_binary64_2121` `flip3-+_binary64_2127` `flip-+_binary64_2098`
22×	`associate-/l*_binary64_2069`
16×	`associate-/r*_binary64_2068` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`pow1_binary64_2185` `unswap-sqr_binary64_2092`
5×	`associate-/l/_binary64_2071`
4×	`add-log-exp_binary64_2163`
3×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-*r/_binary64_2066`
2×	`flip3--_binary64_2128` `flip--_binary64_2099`
1×	`pow-prod-down_binary64_2195` `frac-times_binary64_2134` `associate-l/_binary64_2067` `-commutative_binary64_2055`

Counts

4 → 497

Calls

4 calls:

156.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
21.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
14.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 41545 to 19607 computations (52.8% saved)

series7.1s (15.5%)

Error

5.8b

Counts

4 → 68

Calls

4 calls:

5.2s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
1.2s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
278.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
129.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 20450 to 13822 computations (32.4% saved)

simplify334.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

565 → 565

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5474	42899

prune3.0s (6.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	558	7	565
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	563	10	573

Error

5.8b

Counts

573 → 10

Compiler

Compiled 45262 to 21555 computations (52.4% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i)))))
0.1b	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (*.f64 i 2)) 1))))
35.6b	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))
36.4b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite1.0s (2.3%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

222×	`*-un-lft-identity_binary64_2124`
178×	`times-frac_binary64_2130`
96×	`associate-r_binary64_2064`
94×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
87×	`add-sqr-sqrt_binary64_2146`
78×	`add-cube-cbrt_binary64_2159`
64×	`distribute-lft-out_binary64_2075`
43×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
25×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
20×	`associate-/r/_binary64_2070`
18×	`distribute-lft-out--_binary64_2076`
13×	`associate-/r*_binary64_2068`
12×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
10×	`div-inv_binary64_2121` `associate-l_binary64_2065`
7×	`associate-/l/_binary64_2071`
6×	`pow1_binary64_2185`
5×	`associate-/l*_binary64_2069`
4×	`add-log-exp_binary64_2163` `associate-*r/_binary64_2066`
3×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `unswap-sqr_binary64_2092`
2×	`frac-times_binary64_2134` `associate-*l/_binary64_2067`
1×	`pow-prod-down_binary64_2195` `*-commutative_binary64_2055`

Counts

4 → 247

Calls

4 calls:

60.0ms	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (*.f64 i 2)) 1))))
48.0ms	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i)))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))
10.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 20373 to 9404 computations (53.8% saved)

series9.9s (21.6%)

Error

3.5b

Counts

4 → 68

Calls

4 calls:

5.2s	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i)))))
4.0s	(.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (*.f64 i 2)) 1))))
268.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
130.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))

Compiler

Compiled 24288 to 16712 computations (31.2% saved)

simplify191.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5672	22496

prune1.2s (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	317	8	325

Error

0.2b

Counts

325 → 8

Compiler

Compiled 24160 to 11759 computations (51.3% saved)

regimes2.0s (4.5%)

Accuracy

Total 10.6b remaining (92.9%)

Threshold costs 0b (0%)

Compiler

Compiled 35432 to 20341 computations (42.6% saved)

bsearch96.0ms (0.2%)

Steps

Iters	Range		Point
9	3.2047085575109094e+212	8.454765569088304e+218	3.2397109221427535e+212
5	2.3904465960765875e+139	7.470213704441826e+139	7.353764786069445e+139
6	6.083081383258568e+97	3.76718600259929e+98	6.152445749605528e+97

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	127
1	62	127

Compiler

Compiled 172 to 110 computations (36% saved)

end0.0ms (0%)

sample5.5s (12%)

Algorithm

1×

intervals

Results

669.0ms	8000×	body	128	valid
172.0ms	8000×	pre	128	true

Compiler

Compiled 8898 to 5121 computations (42.4% saved)

Details

analyze175.0ms (0.4%)

sample49.0ms (0.1%)

simplify42.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite972.0ms (2.1%)

series10.1s (21.9%)

simplify205.0ms (0.4%)

prune1.2s (2.5%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune12.0ms (0%)

localize19.0ms (0%)

rewrite2.7s (5.9%)

series7.1s (15.5%)

simplify334.0ms (0.7%)

prune3.0s (6.5%)

localize23.0ms (0%)

rewrite1.0s (2.3%)

series9.9s (21.6%)

simplify191.0ms (0.4%)

prune1.2s (2.6%)

regimes2.0s (4.5%)

bsearch96.0ms (0.2%)

simplify14.0ms (0%)

end0.0ms (0%)

sample5.5s (12%)

Profiling