Details

analyze408.0ms (3.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4733	38
1	4733	38
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample29.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms	196×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	28×	body	1024	valid
2.0ms	18×	body	512	valid
1.0ms	13×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify254.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	5018	19

prune2.0ms (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

14.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite117.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

58×	`*-un-lft-identity_binary64_2124`
26×	`add-sqr-sqrt_binary64_2146`
25×	`times-frac_binary64_2130`
19×	`distribute-lft-out_binary64_2075`
14×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
5×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-sub_binary64_2129` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
1×	`sum-log_binary64_2215` `associate-+l-_binary64_2059` `+-commutative_binary64_2054` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

2 → 65

Calls

2 calls:

22.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1500 to 803 computations (46.5% saved)

series466.0ms (4.2%)

Error

0.1b

Counts

2 → 44

Calls

2 calls:

233.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
156.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 3588 to 2887 computations (19.5% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	3204
1	4957	3204

prune136.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Error

0.1b

Counts

110 → 3

Compiler

Compiled 2841 to 1741 computations (38.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))
0.1b	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
3.5b	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)

rewrite171.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

61×	`*-un-lft-identity_binary64_2124`
32×	`add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130`
23×	`add-cube-cbrt_binary64_2159`
21×	`associate-r_binary64_2064` `distribute-lft-out_binary64_2075`
16×	`add-exp-log_binary64_2162`
10×	`add-cbrt-cube_binary64_2160`
6×	`pow1_binary64_2185`
5×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-/r*_binary64_2068`
4×	`div-exp_binary64_2175` `prod-exp_binary64_2173` `associate-/r/_binary64_2070`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `unswap-sqr_binary64_2092` `associate-/l*_binary64_2069`
2×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `flip3--_binary64_2128` `frac-times_binary64_2134` `flip--_binary64_2099` `associate-*l/_binary64_2067` `div-inv_binary64_2121`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow-prod-down_binary64_2195` `un-div-inv_binary64_2122` `associate-r/_binary64_2066` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `-commutative_binary64_2055` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `frac-2neg_binary64_2135` `clear-num_binary64_2123`

Counts

3 → 102

Calls

3 calls:

17.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
14.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)
10.0ms	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 2485 to 1729 computations (30.4% saved)

series617.0ms (5.5%)

Error

0.1b

Counts

3 → 66

Calls

3 calls:

236.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta)))) 1)
154.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (+.f64 2 beta))))
125.0ms	(/.f64 1 (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 5230 to 4180 computations (20.1% saved)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5017	4347

prune208.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	168	3	171

Error

0.1b

Counts

171 → 3

Compiler

Compiled 4362 to 2826 computations (35.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
0.2b	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
0.4b	(/.f64 4 (*.f64 alpha alpha))
3.0b	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))

rewrite442.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

84×	`add-sqr-sqrt_binary64_2146`
76×	`times-frac_binary64_2130`
62×	`*-un-lft-identity_binary64_2124`
58×	`add-cube-cbrt_binary64_2159`
33×	`cancel-sign-sub-inv_binary64_2090`
26×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-l_binary64_2065`
19×	`associate-r_binary64_2064`
14×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
13×	`pow1_binary64_2185` `swap-sqr_binary64_2091`
9×	`add-log-exp_binary64_2163` `div-inv_binary64_2121`
7×	`frac-sub_binary64_2133` `prod-exp_binary64_2173` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `cbrt-unprod_binary64_2157`
6×	`frac-add_binary64_2132` `unswap-sqr_binary64_2092`
5×	`flip3--_binary64_2128` `frac-times_binary64_2134` `flip--_binary64_2099` `associate-*r/_binary64_2066`
4×	`associate-*l/_binary64_2067` `difference-of-squares_binary64_2093`
3×	`sub-neg_binary64_2117` `associate-/l*_binary64_2069`
2×	`diff-log_binary64_2216` `distribute-lft-out--_binary64_2076` `pow-prod-down_binary64_2195` `*-commutative_binary64_2055`
1×	`sum-log_binary64_2215` `flip3-+_binary64_2127` `flip-+_binary64_2098` `sub-div_binary64_2131` `associate--l+_binary64_2061` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/r*_binary64_2068` `pow2_binary64_2205` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097`

Counts

4 → 186

Calls

4 calls:

15.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
14.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
13.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
4.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 7837 to 4169 computations (46.8% saved)

series738.0ms (6.6%)

Error

0.1b

Counts

4 → 28

Calls

4 calls:

486.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
104.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
89.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
25.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 2461 to 1726 computations (29.9% saved)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4971	3946
1	4971	3946

prune368.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	214	3	217

Error

0.1b

Counts

217 → 3

Compiler

Compiled 7919 to 4291 computations (45.8% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.4b	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
9.5b	(/.f64 beta (*.f64 alpha alpha))
11.1b	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
18.2b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

rewrite1.6s (14.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

123×	`frac-add_binary64_2132`
79×	`associate-*r/_binary64_2066`
63×	`add-log-exp_binary64_2163`
49×	`frac-sub_binary64_2133`
37×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
33×	`sum-log_binary64_2215`
24×	`*-un-lft-identity_binary64_2124`
22×	`add-exp-log_binary64_2162`
15×	`add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130`
14×	`add-cbrt-cube_binary64_2160`
13×	`add-cube-cbrt_binary64_2159` `associate-/r*_binary64_2068`
12×	`diff-log_binary64_2216`
8×	`div-exp_binary64_2175`
7×	`frac-times_binary64_2134` `associate-*l/_binary64_2067`
6×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
4×	`pow1_binary64_2185` `prod-exp_binary64_2173` `cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `distribute-lft-out_binary64_2075`
3×	`cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076`
2×	`pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `unpow3_binary64_2190` `cube-mult_binary64_2154` `sqr-pow_binary64_2096` `clear-num_binary64_2123` `div-inv_binary64_2121`
1×	`flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `associate--l+_binary64_2061` `associate--r+_binary64_2060` `associate-+r+_binary64_2056` `+-commutative_binary64_2054`

Counts

4 → 161

Calls

4 calls:

55.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
31.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
8.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
5.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 22551 to 12871 computations (42.9% saved)

series1.1s (10%)

Error

Counts

4 → 36

Calls

4 calls:

530.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
303.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))
128.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
81.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 5518 to 3776 computations (31.6% saved)

simplify173.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5268	20905

prune1.5s (13%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	198	2	200

Error

Counts

200 → 2

Compiler

Compiled 21474 to 12572 computations (41.5% saved)

regimes516.0ms (4.6%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Compiler

Compiled 6963 to 5098 computations (26.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	176	144
1	176	144

end0.0ms (0%)

sample2.0s (18.2%)

Algorithm

1×

intervals

Results

224.0ms	5994×	body	128	valid
148.0ms	1022×	body	1024	valid
140.0ms	8000×	pre	128	true
62.0ms	564×	body	512	valid
23.0ms	327×	body	256	valid
20.0ms	93×	body	2048	valid

Compiler

Compiled 1446 to 1045 computations (27.7% saved)

Details

analyze408.0ms (3.6%)

sample29.0ms (0.3%)

simplify254.0ms (2.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite117.0ms (1%)

series466.0ms (4.2%)

simplify79.0ms (0.7%)

prune136.0ms (1.2%)

localize10.0ms (0.1%)

rewrite171.0ms (1.5%)

series617.0ms (5.5%)

simplify87.0ms (0.8%)

prune208.0ms (1.9%)

localize17.0ms (0.1%)

rewrite442.0ms (3.9%)

series738.0ms (6.6%)

simplify105.0ms (0.9%)

prune368.0ms (3.3%)

localize38.0ms (0.3%)

rewrite1.6s (14.3%)

series1.1s (10%)

simplify173.0ms (1.5%)

prune1.5s (13%)

regimes516.0ms (4.6%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.0s (18.2%)

Profiling