Details

analyze2.0ms (0%)

Algorithm

1×

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)

sample26.0ms (0%)

Algorithm

1×

intervals

Results

7.0ms	190×	body	128	valid
5.0ms	37×	body	1024	valid
4.0ms	256×	pre	128	true
2.0ms	18×	body	512	valid
1.0ms	5×	body	2048	valid
0.0ms	6×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify353.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (248.0ms)

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

16.3b

Counts

2 → 1

Compiler

Compiled 13 to 11 computations (15.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

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×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `flip3-+_binary64_2127` `div-sub_binary64_2129` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-+l-_binary64_2059` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 65

Calls

4 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series398.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

240.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
158.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1994 to 1666 computations (16.4% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5023	3850

prune576.0ms (0.2%)

Pruning

60 alts after pruning (59 fresh and 1 done)

	Pruned	Kept	Total
New	54	59	113
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	54	60	114

Error

0.0b

Counts

114 → 60

Compiler

Compiled 3992 to 2554 computations (36% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite79.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_2124`
54×	`add-sqr-sqrt_binary64_2146`
37×	`times-frac_binary64_2130`
27×	`add-cube-cbrt_binary64_2159`
24×	`distribute-lft-out_binary64_2075`
16×	`cancel-sign-sub-inv_binary64_2090`
11×	`add-log-exp_binary64_2163`
10×	`difference-of-squares_binary64_2093` `associate-/r*_binary64_2068`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/l*_binary64_2069`
5×	`distribute-lft-out--_binary64_2076`
4×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `diff-log_binary64_2216` `associate--r+_binary64_2060` `difference-of-sqr-1_binary64_2094`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `sub-neg_binary64_2117`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `frac-sub_binary64_2133` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`associate--r-_binary64_2063`

Counts

4 → 128

Calls

8 calls:

35.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))

series584.0ms (0.2%)

Counts

4 → 75

Calls

4 calls:

247.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
120.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
113.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
104.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 3342 to 2702 computations (19.2% saved)

simplify86.0ms (0%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5317	5905

localize2.0ms (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

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

17.7b	(/.f64 (-.f64 beta alpha) (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))
3.3b	(+.f64 (.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2)) 1)
0.1b	(.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.1b	(.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2))
3.3b	(+.f64 (.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2)) 1)
17.7b	(/.f64 (-.f64 beta alpha) (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))

rewrite103.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2146`
71×	`*-un-lft-identity_binary64_2124`
41×	`times-frac_binary64_2130`
34×	`add-cube-cbrt_binary64_2159`
30×	`associate-l_binary64_2065`
21×	`difference-of-squares_binary64_2093`
13×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`cancel-sign-sub-inv_binary64_2090`
11×	`distribute-lft-out--_binary64_2076` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
10×	`associate-r_binary64_2064` `associate-+l+_binary64_2057`
7×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098`
6×	`swap-sqr_binary64_2091` `add-log-exp_binary64_2163` `frac-times_binary64_2134`
5×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/l*_binary64_2069`
4×	`associate-/r/_binary64_2070` `associate-/r_binary64_2068` `associate--l+_binary64_2061` `sub-neg_binary64_2117` `associate-r/_binary64_2066`
3×	`unswap-sqr_binary64_2092` `associate-*l/_binary64_2067` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `*-commutative_binary64_2055` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `pow-prod-up_binary64_2194` `sum-log_binary64_2215` `pow-plus_binary64_2187` `+-commutative_binary64_2054` `pow2_binary64_2205` `pow-sqr_binary64_2097` `div-sub_binary64_2129` `frac-2neg_binary64_2135`

Counts

4 → 169

Calls

8 calls:

30.0ms	(.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2))
27.0ms	(+.f64 (.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2)) 1)
16.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))
10.0ms	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.0ms	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))

series1.4s (0.5%)

Counts

4 → 80

Calls

4 calls:

727.0ms	(+.f64 (.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2)) 1)
420.0ms	(.f64 (/.f64 (-.f64 beta alpha) (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (-.f64 (+.f64 alpha beta) 2))
170.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))
100.0ms	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))

Compiler

Compiled 4461 to 3747 computations (16% saved)

simplify98.0ms (0%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4961	9674
1	4961	9674

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64_2124`
84×	`add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130`
65×	`sqrt-prod_binary64_2140`
51×	`distribute-lft-out_binary64_2075`
46×	`associate-r_binary64_2064`
44×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`associate-/l_binary64_2069` `associate-l*_binary64_2065`
6×	`unswap-sqr_binary64_2092` `sqrt-div_binary64_2141`
5×	`associate-/r*_binary64_2068`
4×	`associate-/r/_binary64_2070` `pow1_binary64_2185`
3×	`flip--_binary64_2099` `flip3--_binary64_2128`
2×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `associate-*l/_binary64_2067` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-r/_binary64_2066` `frac-2neg_binary64_2135`

Counts

2 → 147

Calls

4 calls:

32.0ms	(*.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2)))
12.0ms	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(*.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2)))

series212.0ms (0.1%)

Counts

2 → 27

Calls

2 calls:

148.0ms	(*.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2)))
63.0ms	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 1108 to 924 computations (16.6% saved)

simplify87.0ms (0%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	4233
1	4961	4233

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (+.f64 alpha 2) 2)
0.0b	(-.f64 (+.f64 (/.f64 beta (+.f64 alpha 2)) (/.f64 (.f64 beta alpha) (pow.f64 (+.f64 alpha 2) 2))) (+.f64 (/.f64 alpha (+.f64 alpha 2)) (+.f64 (/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3)) (/.f64 (.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2)))))
0.0b	(+.f64 (/.f64 alpha (+.f64 alpha 2)) (+.f64 (/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3)) (/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2))))
0.0b	(/.f64 alpha (+.f64 alpha 2))
1.8b	(+.f64 (/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3)) (/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2)))
3.3b	(/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2))
4.1b	(/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3))
7.4b	(/.f64 (*.f64 beta alpha) (pow.f64 (+.f64 alpha 2) 2))

rewrite80.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64_2162`
38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
32×	`associate-/r*_binary64_2068`
24×	`unpow-prod-down_binary64_2203`
23×	`add-cbrt-cube_binary64_2160`
21×	`div-exp_binary64_2175`
18×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
15×	`prod-exp_binary64_2173`
11×	`distribute-lft-out_binary64_2075`
8×	`cube-prod_binary64_2152`
7×	`cbrt-undiv_binary64_2158` `pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
6×	`add-log-exp_binary64_2163` `sqr-pow_binary64_2096`
5×	`unpow2_binary64_2189` `cbrt-unprod_binary64_2157`
4×	`pow1_binary64_2185`
3×	`clear-num_binary64_2123` `cube-mult_binary64_2154` `associate-/l*_binary64_2069` `div-inv_binary64_2121` `frac-2neg_binary64_2135`
2×	`unpow3_binary64_2190` `associate-/r/_binary64_2070` `flip3-+_binary64_2127` `cube-div_binary64_2153` `flip-+_binary64_2098`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `frac-add_binary64_2132`

Counts

4 → 142

Calls

8 calls:

32.0ms	(+.f64 (/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3)) (/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2)))
11.0ms	(/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3))
8.0ms	(/.f64 (*.f64 beta alpha) (pow.f64 (+.f64 alpha 2) 2))
8.0ms	(/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2))
0.0ms	(/.f64 alpha (+.f64 alpha 2))

series609.0ms (0.2%)

Counts

4 → 37

Calls

4 calls:

210.0ms	(+.f64 (/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3)) (/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2)))
152.0ms	(/.f64 (.f64 beta (.f64 beta alpha)) (pow.f64 (+.f64 alpha 2) 3))
130.0ms	(/.f64 (*.f64 beta alpha) (pow.f64 (+.f64 alpha 2) 2))
117.0ms	(/.f64 (*.f64 beta beta) (pow.f64 (+.f64 alpha 2) 2))

Compiler

Compiled 2997 to 2286 computations (23.7% saved)

simplify67.0ms (0%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4967	3067
1	4967	3067

prune14.2s (4.8%)

Pruning

351 alts after pruning (346 fresh and 5 done)

	Pruned	Kept	Total
New	502	303	805
Fresh	11	43	54
Picked	0	0	0
Done	1	5	6
Total	514	351	865

Error

0.0b

Counts

865 → 351

Compiler

Compiled 33704 to 20272 computations (39.9% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64_2124`
53×	`add-sqr-sqrt_binary64_2146`
50×	`times-frac_binary64_2130`
35×	`add-cube-cbrt_binary64_2159`
33×	`distribute-lft-out_binary64_2075`
21×	`associate-r_binary64_2064`
19×	`add-exp-log_binary64_2162`
13×	`add-cbrt-cube_binary64_2160`
10×	`associate-/r*_binary64_2068`
7×	`pow1_binary64_2185`
6×	`associate-/r/_binary64_2070` `associate-/l*_binary64_2069` `add-log-exp_binary64_2163`
5×	`div-exp_binary64_2175`
4×	`difference-of-squares_binary64_2093` `prod-exp_binary64_2173`
3×	`cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `unswap-sqr_binary64_2092` `associate-l_binary64_2065` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `difference-of-sqr-1_binary64_2094` `1-exp_binary64_2168` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `un-div-inv_binary64_2122` `distribute-lft-out--_binary64_2076` `-commutative_binary64_2055` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `associate-r/_binary64_2066` `inv-pow_binary64_2209`

Counts

4 → 143

Calls

8 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
14.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
11.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0ms	(-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))

series440.0ms (0.1%)

Counts

4 → 70

Calls

4 calls:

117.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
114.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
110.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
99.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 3200 to 2577 computations (19.5% saved)

simplify107.0ms (0%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	4311
1	4942	4311

localize3.0ms (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

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.0b	(+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)))
0.0b	(pow.f64 (+.f64 beta alpha) 6)
0.1b	(.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))
1.1b	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64))
7.9b	(+.f64 (.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)))) (-.f64 (+.f64 alpha beta) 2)) 1)
28.2b	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))))

rewrite521.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

842×	`frac-times_binary64_2134`
705×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
382×	`associate-*r/_binary64_2066`
320×	`frac-add_binary64_2132`
221×	`associate-*l/_binary64_2067`
117×	`pow1_binary64_2185`
68×	`*-un-lft-identity_binary64_2124`
51×	`add-sqr-sqrt_binary64_2146`
41×	`times-frac_binary64_2130`
36×	`pow-prod-up_binary64_2194`
28×	`add-cube-cbrt_binary64_2159`
27×	`associate-l_binary64_2065`
24×	`pow-prod-down_binary64_2195`
23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`pow-sqr_binary64_2097`
18×	`pow-plus_binary64_2187`
13×	`pow2_binary64_2205`
11×	`distribute-lft-out_binary64_2075`
10×	`prod-exp_binary64_2173` `distribute-rgt-in_binary64_2074` `associate-+l+_binary64_2057` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157`
9×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
6×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
5×	`associate-/l*_binary64_2069`
4×	`associate-/r/_binary64_2070` `associate-/r_binary64_2068` `associate-r*_binary64_2064`
3×	`unswap-sqr_binary64_2092`
2×	`cbrt-undiv_binary64_2158` `*-commutative_binary64_2055` `associate--l+_binary64_2061` `sub-neg_binary64_2117` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `sum-log_binary64_2215` `swap-sqr_binary64_2091` `+-commutative_binary64_2054` `div-sub_binary64_2129` `frac-2neg_binary64_2135`

Counts

4 → 585

Calls

8 calls:

170.0ms	(+.f64 (.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)))) (-.f64 (+.f64 alpha beta) 2)) 1)
82.0ms	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))))
30.0ms	(.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))
13.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64))
0.0ms	(pow.f64 (+.f64 beta alpha) 6)

series5.3s (1.8%)

Counts

4 → 54

Calls

4 calls:

4.4s	(+.f64 (.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)))) (-.f64 (+.f64 alpha beta) 2)) 1)
646.0ms	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64)) (+.f64 (.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (.f64 (+.f64 beta alpha) (+.f64 beta alpha))) (+.f64 (.f64 4 4) (.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))))
165.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 6) -64))
44.0ms	(.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))

Compiler

Compiled 7241 to 5746 computations (20.6% saved)

simplify547.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

639 → 639

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5106	70682

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 beta (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_2124`
19×	`add-sqr-sqrt_binary64_2146`
15×	`cbrt-prod_binary64_2155`
9×	`distribute-lft-out_binary64_2075`
8×	`add-cube-cbrt_binary64_2159`
6×	`cbrt-div_binary64_2156` `add-log-exp_binary64_2163`
4×	`difference-of-squares_binary64_2093` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`cancel-sign-sub-inv_binary64_2090` `pow1/3_binary64_2206` `flip3-+_binary64_2127` `flip-+_binary64_2098` `times-frac_binary64_2130`
2×	`difference-of-sqr-1_binary64_2094`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `sub-neg_binary64_2117`

Counts

4 → 66

Calls

8 calls:

22.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.0ms	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (/.f64 beta (cbrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))

series674.0ms (0.2%)

Counts

4 → 57

Calls

4 calls:

190.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
182.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
180.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
121.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

Compiler

Compiled 4567 to 3648 computations (20.1% saved)

simplify56.0ms (0%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5137	2841

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))
0.2b	(.f64 (sqrt.f64 (-.f64 beta alpha)) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))))
0.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
0.1b	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))
0.6b	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))

rewrite46.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2124`
18×	`cbrt-div_binary64_2156`
15×	`cbrt-prod_binary64_2155` `add-exp-log_binary64_2162`
12×	`pow1_binary64_2185`
9×	`distribute-lft-out_binary64_2075` `add-cube-cbrt_binary64_2159` `pow1/3_binary64_2206` `add-sqr-sqrt_binary64_2146` `pow-flip_binary64_2198` `flip3-+_binary64_2127` `flip-+_binary64_2098`
8×	`associate-/r/_binary64_2070`
7×	`add-cbrt-cube_binary64_2160`
4×	`add-log-exp_binary64_2163` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`associate-/l*_binary64_2069` `prod-exp_binary64_2173` `times-frac_binary64_2130`
2×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `pow-prod-up_binary64_2194` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `pow-sqr_binary64_2097` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `associate-/r*_binary64_2068` `pow-plus_binary64_2187` `pow2_binary64_2205` `div-inv_binary64_2121` `inv-pow_binary64_2209` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 88

Calls

8 calls:

18.0ms	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.0ms	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))

series1.8s (0.6%)

Counts

4 → 54

Calls

4 calls:

1.3s	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
169.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
165.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
163.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 6122 to 4912 computations (19.8% saved)

simplify71.0ms (0%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4933	3740
1	4933	3740

prune1.3min (26.9%)

Pruning

704 alts after pruning (696 fresh and 8 done)

	Pruned	Kept	Total
New	746	371	1117
Fresh	16	325	341
Picked	0	0	0
Done	2	8	10
Total	764	704	1468

Error

0.0b

Counts

1468 → 704

Compiler

Compiled 119740 to 59379 computations (50.4% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 (-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) 2)
0.0b	(-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
0.9b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite72.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_2124`
57×	`add-sqr-sqrt_binary64_2146`
38×	`times-frac_binary64_2130`
28×	`add-cube-cbrt_binary64_2159`
21×	`distribute-lft-out_binary64_2075` `associate-r_binary64_2064`
17×	`add-exp-log_binary64_2162`
11×	`log-pow_binary64_2213` `add-cbrt-cube_binary64_2160`
10×	`exp-prod_binary64_2176`
8×	`difference-of-squares_binary64_2093` `pow1_binary64_2185`
7×	`log-prod_binary64_2210`
6×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
5×	`associate-/r*_binary64_2068`
4×	`associate-/r/_binary64_2070` `prod-exp_binary64_2173` `difference-of-sqr-1_binary64_2094` `div-exp_binary64_2175` `exp-sum_binary64_2170`
3×	`unswap-sqr_binary64_2092` `associate-/l_binary64_2069` `associate-l*_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `distribute-lft-out--_binary64_2076` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `1-exp_binary64_2168` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `clear-num_binary64_2123` `flip3--_binary64_2128` `un-div-inv_binary64_2122` `rem-log-exp_binary64_2165` `exp-diff_binary64_2172` `-commutative_binary64_2055` `diff-log_binary64_2216` `pow-flip_binary64_2198` `associate-r/_binary64_2066` `log-div_binary64_2211` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 133

Calls

8 calls:

19.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
14.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0ms	(-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))

series530.0ms (0.2%)

Counts

4 → 69

Calls

4 calls:

187.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
118.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
116.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
109.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 3369 to 2740 computations (18.7% saved)

simplify128.0ms (0%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4936	4353
1	4936	4353

localize3.0ms (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

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(-.f64 (.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 (-.f64 (.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
0.3b	(*.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
0.3b	(.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite89.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64_2124`
66×	`sqrt-prod_binary64_2140`
59×	`add-sqr-sqrt_binary64_2146`
52×	`times-frac_binary64_2130`
48×	`associate-r_binary64_2064`
35×	`add-cube-cbrt_binary64_2159`
27×	`distribute-lft-out_binary64_2075`
13×	`pow1_binary64_2185`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
4×	`difference-of-squares_binary64_2093` `pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `associate-l_binary64_2065` `prod-exp_binary64_2173` `associate-*r/_binary64_2066` `cbrt-unprod_binary64_2157`
3×	`cancel-sign-sub-inv_binary64_2090` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`*-commutative_binary64_2055` `difference-of-sqr-1_binary64_2094`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `associate-*l/_binary64_2067` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `frac-times_binary64_2134` `inv-pow_binary64_2209`

Counts

4 → 142

Calls

8 calls:

29.0ms	(.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
16.0ms	(*.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
9.0ms	(sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
0.0ms	(/.f64 (-.f64 (.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)

series475.0ms (0.2%)

Counts

4 → 56

Calls

4 calls:

138.0ms	(*.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
119.0ms	(.f64 (.f64 beta (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))) (sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2))))
115.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
103.0ms	(sqrt.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 3246 to 2597 computations (20% saved)

simplify109.0ms (0%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4935	4335
1	4935	4335

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))
0.1b	(.f64 (.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))) (-.f64 (+.f64 alpha beta) 2))
0.0b	(+.f64 (sqrt.f64 beta) (sqrt.f64 alpha))
0.0b	(-.f64 (sqrt.f64 beta) (sqrt.f64 alpha))
0.1b	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))
0.2b	(*.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2)))
4.7b	(+.f64 (.f64 (.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))) (-.f64 (+.f64 alpha beta) 2)) 1)

rewrite198.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64_2124`
216×	`add-sqr-sqrt_binary64_2146`
162×	`times-frac_binary64_2130`
100×	`sqrt-prod_binary64_2140`
74×	`distribute-lft-out_binary64_2075`
71×	`difference-of-squares_binary64_2093`
64×	`distribute-lft-out--_binary64_2076`
62×	`add-cube-cbrt_binary64_2159`
60×	`associate-r_binary64_2064`
31×	`associate-l_binary64_2065`
20×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
14×	`associate-/l*_binary64_2069`
11×	`associate-/r*_binary64_2068`
10×	`associate-+l+_binary64_2057`
8×	`associate-/r/_binary64_2070`
6×	`cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `pow1_binary64_2185` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
5×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
4×	`unswap-sqr_binary64_2092` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `flip3--_binary64_2128`
2×	`clear-num_binary64_2123` `associate--l+_binary64_2061` `sub-neg_binary64_2117` `frac-2neg_binary64_2135`
1×	`pow-prod-down_binary64_2195` `sum-log_binary64_2215` `-commutative_binary64_2055` `associate-l/_binary64_2067` `+-commutative_binary64_2054` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `div-sub_binary64_2129`

Counts

4 → 273

Calls

8 calls:

70.0ms	(*.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2)))
42.0ms	(+.f64 (.f64 (.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))) (-.f64 (+.f64 alpha beta) 2)) 1)
16.0ms	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))
14.0ms	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(-.f64 (sqrt.f64 beta) (sqrt.f64 alpha))

series472.0ms (0.2%)

Counts

4 → 37

Calls

4 calls:

175.0ms	(+.f64 (.f64 (.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))) (-.f64 (+.f64 alpha beta) 2)) 1)
141.0ms	(*.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2)))
82.0ms	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (-.f64 (+.f64 beta alpha) 2))
74.0ms	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 2419 to 1909 computations (21.1% saved)

simplify131.0ms (0%)

Algorithm

1×	egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5067	10610

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (-.f64 beta alpha)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (cbrt.f64 (-.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (cbrt.f64 (-.f64 (+.f64 beta alpha) 2))))))
0.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (cbrt.f64 (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (cbrt.f64 (-.f64 (+.f64 beta alpha) 2)))))
0.1b	(/.f64 (sqrt.f64 (-.f64 beta alpha)) (/.f64 (cbrt.f64 (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4)) (cbrt.f64 (-.f64 (+.f64 beta alpha) 2))))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
0.7b	(cbrt.f64 (-.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
18.3b	(cbrt.f64 (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_2124`
20×	`cbrt-prod_binary64_2155`
11×	`add-sqr-sqrt_binary64_2146`
8×	`cbrt-div_binary64_2156` `add-cube-cbrt_binary64_2159`
7×	`distribute-lft-out_binary64_2075`
4×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `pow1/3_binary64_2206` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 60

Calls

8 calls:

10.0ms	(cbrt.f64 (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))
7.0ms	(cbrt.f64 (-.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.0ms	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))

series646.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

199.0ms	(cbrt.f64 (-.f64 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)) 4))
175.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
159.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
113.0ms	(cbrt.f64 (-.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 4752 to 3472 computations (26.9% saved)

simplify94.0ms (0%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4938	2092
1	4938	2092

prune1.0min (20.5%)

Pruning

933 alts after pruning (921 fresh and 12 done)

	Pruned	Kept	Total
New	540	278	818
Fresh	48	643	691
Picked	0	0	0
Done	1	12	13
Total	589	933	1522

Error

0.0b

Counts

1522 → 933

Compiler

Compiled 21071 to 11719 computations (44.4% saved)

simplify2.8s (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	10796	171720

regimes37.9s (12.8%)

Compiler: Compiled 562100 to 327474 computations (41.7% saved)

bsearch160.0ms (0.1%)

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

regimes3.2s (1.1%)

Compiler: Compiled 48740 to 30909 computations (36.6% saved)

bsearch16.0ms (0%)

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

regimes1.3s (0.4%)

Compiler: Compiled 14175 to 10995 computations (22.4% saved)

bsearch5.0ms (0%)

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

regimes300.0ms (0.1%)

Compiler: Compiled 2100 to 1950 computations (7.1% saved)

bsearch1.0ms (0%)

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

regimes249.0ms (0.1%)

Compiler: Compiled 1605 to 1521 computations (5.2% saved)

bsearch1.0ms (0%)

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

regimes79.0ms (0%)

Compiler: Compiled 236 to 248 computations (-5.1% saved)

bsearch23.0ms (0%)

Steps

Iters	Range		Point
10	6.168863799812995e+31	5.239632002753187e+48	6.280321599555968e+31

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes77.0ms (0%)

Compiler: Compiled 210 to 224 computations (-6.7% saved)

bsearch27.0ms (0%)

Steps

Iters	Range		Point
10	6.168863799812995e+31	5.239632002753187e+48	1.1580978541201579e+32

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0%)

Compiler: Compiled 30 to 50 computations (-66.7% saved)

bsearch0.0ms (0%)

regimes29.0ms (0%)

Compiler: Compiled 12 to 32 computations (-166.7% saved)

bsearch16.0ms (0%)

Steps

Iters	Range		Point
8	0.030276741374203713	560.209298389477	1.9929106022751548

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0%)

Accuracy

Total 0.5b remaining (96.5%)

Threshold costs 0.5b (96.5%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch13.0ms (0%)

Compiler: Compiled 307 to 228 computations (25.7% saved)

simplify25.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	603	452
1	603	452

end0.0ms (0%)

sample1.3min (26%)

Algorithm

1×

intervals

Results

212.0ms	5969×	body	128	valid
144.0ms	8000×	pre	128	true
139.0ms	1049×	body	1024	valid
57.0ms	571×	body	512	valid
21.0ms	314×	body	256	valid
16.0ms	97×	body	2048	valid

Compiler

Compiled 113303 to 66133 computations (41.6% saved)

Pareto

0.9465523493839461