Details

Time bar (total: 5.0s)

sample27.0ms

Algorithm
intervals
Results
6.0ms27×body1280valid
5.0ms192×body80valid
3.0ms256×pre80true
1.0ms14×body640valid
1.0ms14×body320valid
0.0ms9×body160valid

simplify81.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0206
1346
2526
3736
41236
51846
62506
72876
83496
94376
105746
116546
127126
137856
1410756
1511506
1611936
1712136
1812216
1912216

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
50×times-frac
47×add-sqr-sqrt
34×distribute-lft-out
31×fma-def
25×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log associate-/r/ add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×pow1 expm1-log1p-u div-sub log1p-expm1-u div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l- flip3-- frac-2neg div-exp clear-num sum-log flip--
Counts
2 → 100
Calls
2 calls:
45.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
170.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series114.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0335555
11087529
25002525

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
1.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
182×*-un-lft-identity
91×times-frac
85×add-sqr-sqrt
80×add-cube-cbrt
63×prod-diff
60×distribute-lft-out
21×fma-neg
12×associate-/r/
10×associate-/r*
7×add-exp-log add-cbrt-cube
6×flip3-+ flip-+ div-inv associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 179
Calls
3 calls:
35.0ms
(/ alpha (+ (+ alpha beta) 2.0))
35.0ms
(/ beta (+ (+ alpha beta) 2.0))
206.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series174.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ alpha (+ (+ alpha beta) 2.0))
47.0ms
(/ beta (+ (+ alpha beta) 2.0))
78.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04931766
116231302
250021263

prune325.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
106×times-frac
93×add-sqr-sqrt
88×add-cube-cbrt
63×cbrt-prod prod-diff distribute-lft-out
21×fma-neg
14×associate-/r/
7×flip3-+ flip-+ div-inv
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 197
Calls
4 calls:
205.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
19.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
141.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
143.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
143.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05092277
114471794
250011714

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.1b
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
84×cbrt-prod
60×times-frac
42×add-sqr-sqrt add-cube-cbrt
36×distribute-lft-out
25×log-pow
24×exp-prod
8×associate-/r/
5×pow1
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u div-inv add-log-exp
3×cbrt-div log-prod pow1/3
1×rem-log-exp
Counts
4 → 134
Calls
4 calls:
17.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
19.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
73.0ms
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
155.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
150.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
156.0ms
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

simplify95.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
02871234
17151171
229371119
350011083

prune486.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

regimes157.0ms

Accuracy

98.9% (0.2b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 16.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04239
14239

end0.0ms

sample645.0ms

Algorithm
intervals
Results
144.0ms5812×body80valid
105.0ms836×body1280valid
91.0ms8000×pre80true
73.0ms742×body640valid
30.0ms378×body320valid
11.0ms232×body160valid