Details

analyze276.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4894	172
1	4894	172
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample39.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	207×	body	128	valid
6.0ms	256×	pre	128	true
5.0ms	21×	body	1024	valid
2.0ms	15×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5371	43

prune6.0ms (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

23.4b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.6b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
18.9b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite393.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

12.1b

Rules

56×	`*-un-lft-identity_binary64_2124`
54×	`times-frac_binary64_2130`
34×	`add-sqr-sqrt_binary64_2146`
30×	`add-cube-cbrt_binary64_2159`
20×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
14×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/r/_binary64_2070`
12×	`distribute-lft-out_binary64_2075`
10×	`associate-/l*_binary64_2069`
9×	`associate-/l/_binary64_2071`
8×	`frac-times_binary64_2134`
7×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `associate-/r*_binary64_2068`
6×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `flip3--_binary64_2128` `flip--_binary64_2099` `cancel-sign-sub-inv_binary64_2090`
5×	`associate-r_binary64_2064`
4×	`associate-l/_binary64_2067` `associate-r/_binary64_2066` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-l_binary64_2065`
3×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `sub-neg_binary64_2117`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055`

Counts

4 → 148

Calls

4 calls:

34.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
22.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
14.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

Compiler

Compiled 6791 to 3352 computations (50.6% saved)

series3.6s (13.8%)

Error

0.0b

Counts

4 → 81

Calls

4 calls:

1.8s	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.2s	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
210.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
114.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

Compiler

Compiled 14215 to 10939 computations (23% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5254	11170

prune539.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	223	6	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	6	230

Error

0.0b

Counts

230 → 6

Compiler

Compiled 10824 to 5752 computations (46.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
1.3b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
1.6b	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)
18.9b	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

rewrite1.7s (6.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

723×	`times-frac_binary64_2130`
442×	`*-un-lft-identity_binary64_2124`
295×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
80×	`associate-/r*_binary64_2068`
74×	`distribute-lft-out_binary64_2075`
53×	`difference-of-squares_binary64_2093`
39×	`associate-/r/_binary64_2070`
27×	`add-exp-log_binary64_2162`
23×	`div-inv_binary64_2121`
18×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
16×	`div-exp_binary64_2175`
15×	`add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069`
5×	`pow1_binary64_2185`
3×	`1-exp_binary64_2168` `rec-exp_binary64_2174`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `flip3--_binary64_2128` `associate-/l/_binary64_2071` `flip--_binary64_2099`
1×	`div-sub_binary64_2129` `sum-log_binary64_2215` `+-commutative_binary64_2054` `diff-log_binary64_2216` `sub-neg_binary64_2117` `cancel-sign-sub-inv_binary64_2090` `inv-pow_binary64_2209` `pow-flip_binary64_2198`

Counts

4 → 398

Calls

4 calls:

93.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)
38.0ms	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
12.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
4.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 22894 to 12304 computations (46.3% saved)

series3.8s (14.5%)

Error

0.0b

Counts

4 → 81

Calls

4 calls:

1.9s	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)
1.3s	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
222.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
107.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 14745 to 11396 computations (22.7% saved)

simplify248.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

479 → 479

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5334	30450

prune1.6s (6.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	478	1	479
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	480	5	485

Error

0.0b

Counts

485 → 5

Compiler

Compiled 26122 to 13854 computations (47% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)) 1)

0.0b

(/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)

0.3b

(/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta))

rewrite263.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

108×	`times-frac_binary64_2130`
96×	`*-un-lft-identity_binary64_2124`
61×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
19×	`associate-/r*_binary64_2068`
18×	`distribute-lft-out_binary64_2075`
16×	`add-exp-log_binary64_2162`
10×	`add-cbrt-cube_binary64_2160`
8×	`div-exp_binary64_2175`
7×	`div-inv_binary64_2121` `associate-/l*_binary64_2069`
5×	`add-log-exp_binary64_2163`
4×	`pow1_binary64_2185` `cbrt-undiv_binary64_2158`
2×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `flip3-+_binary64_2127` `associate-/l/_binary64_2071` `flip-+_binary64_2098`
1×	`inv-pow_binary64_2209` `pow-flip_binary64_2198` `associate-/r/_binary64_2070` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

3 → 134

Calls

3 calls:

26.0ms

(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)) 1)

13.0ms

(/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)

13.0ms

(/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta))

Compiler

Compiled 4087 to 2828 computations (30.8% saved)

series860.0ms (3.3%)

Error

0.0b

Counts

3 → 58

Calls

3 calls:

249.0ms

(/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta))

185.0ms

(/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)

166.0ms

(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))) beta)) 1)

Compiler

Compiled 4390 to 3551 computations (19.1% saved)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5370	5802

prune276.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	192	5	197

Error

0.0b

Counts

197 → 5

Compiler

Compiled 5461 to 3549 computations (35% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
1.6b	(+.f64 (log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)
3.3b	(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
18.9b	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

rewrite440.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

132×	`times-frac_binary64_2130`
105×	`*-un-lft-identity_binary64_2124`
80×	`log-pow_binary64_2213`
78×	`exp-prod_binary64_2176`
66×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
20×	`distribute-lft-out_binary64_2075`
17×	`difference-of-squares_binary64_2093`
12×	`associate-/r/_binary64_2070`
7×	`add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
6×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `div-inv_binary64_2121` `log-prod_binary64_2210`
5×	`div-sub_binary64_2129`
4×	`associate-/l*_binary64_2069`
3×	`associate-/r*_binary64_2068` `associate-+l+_binary64_2057`
2×	`flip3--_binary64_2128` `associate-/l/_binary64_2071` `flip--_binary64_2099` `exp-diff_binary64_2172` `log-div_binary64_2211`
1×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `rem-log-exp_binary64_2165` `sum-log_binary64_2215` `associate-+l-_binary64_2059` `+-commutative_binary64_2054` `diff-log_binary64_2216` `sub-neg_binary64_2117` `cancel-sign-sub-inv_binary64_2090`

Counts

4 → 157

Calls

4 calls:

55.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)
31.0ms	(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
11.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
4.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 8295 to 4246 computations (48.8% saved)

series6.9s (26.4%)

Error

0.0b

Counts

4 → 82

Calls

4 calls:

3.7s	(+.f64 (log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)
2.7s	(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
190.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
106.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 14985 to 11652 computations (22.2% saved)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5168	11566

prune609.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	239	5	244

Error

0.0b

Counts

244 → 5

Compiler

Compiled 12276 to 6464 computations (47.3% saved)

regimes1.2s (4.5%)

Accuracy

Total 1.4b remaining (96.6%)

Threshold costs 0b (0%)

Compiler

Compiled 19717 to 13930 computations (29.4% saved)

bsearch5.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	272	185
1	272	185

end0.0ms (0%)

sample3.0s (11.3%)

Algorithm

1×

intervals

Results

395.0ms	6549×	body	128	valid
183.0ms	8000×	pre	128	true
135.0ms	600×	body	1024	valid
84.0ms	479×	body	512	valid
35.0ms	308×	body	256	valid
18.0ms	64×	body	2048	valid

Compiler

Compiled 2891 to 2024 computations (30% saved)

Details

analyze276.0ms (1.1%)

sample39.0ms (0.2%)

simplify76.0ms (0.3%)

prune6.0ms (0%)

localize12.0ms (0%)

rewrite393.0ms (1.5%)

series3.6s (13.8%)

simplify107.0ms (0.4%)

prune539.0ms (2.1%)

localize15.0ms (0.1%)

rewrite1.7s (6.6%)

series3.8s (14.5%)

simplify248.0ms (0.9%)

prune1.6s (6.2%)

localize10.0ms (0%)

rewrite263.0ms (1%)

series860.0ms (3.3%)

simplify79.0ms (0.3%)

prune276.0ms (1.1%)

localize17.0ms (0.1%)

rewrite440.0ms (1.7%)

series6.9s (26.4%)

simplify110.0ms (0.4%)

prune609.0ms (2.3%)

regimes1.2s (4.5%)

bsearch5.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample3.0s (11.3%)

Profiling