Details

Time bar (total: 13.3s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify78.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
11.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify134.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0149213034
1500212552

prune945.0ms

Filtered
477 candidates to 281 candidates (58.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
18×associate-*r*
16×prod-exp
15×cbrt-undiv associate-*l*
10×associate-/r* associate-/r/
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×flip3-+ flip-+ unswap-sqr
5×rec-exp 1-exp div-inv associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 169
Calls
4 calls:
7.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
31.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
134.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
146.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07642679
150012305

prune362.0ms

Filtered
181 candidates to 116 candidates (64.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
0.7b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
2502×times-frac
1611×*-un-lft-identity
1043×add-sqr-sqrt add-cube-cbrt
507×sqrt-prod
460×cbrt-prod
284×distribute-lft-out
160×associate-/l*
144×associate-/r/
75×flip3-+ flip-+
69×div-inv
42×add-exp-log
25×add-cbrt-cube
22×sqrt-div div-exp
17×associate-/r*
16×cbrt-undiv
14×cbrt-div
5×associate-/l/
4×pow1 frac-times frac-2neg prod-exp clear-num add-log-exp
2×rec-exp 1-exp associate-*r/ associate-*l/ cbrt-unprod
Counts
4 → 1202
Calls
4 calls:
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
29.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
63.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series953.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
239.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
434.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify391.0ms

Algorithm
egg-herbie
Counts
1214 → 1214
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0318541871
1500141317

prune3.2s

Filtered
1214 candidates to 632 candidates (52.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite952.0ms

Algorithm
rewrite-expression-head
Rules
1973×times-frac
1066×*-un-lft-identity
1026×add-sqr-sqrt
779×cbrt-prod
720×add-cube-cbrt
615×associate-*r*
173×distribute-lft-out
97×associate-*l*
84×add-exp-log
74×associate-/r/
63×unswap-sqr
44×cbrt-undiv div-exp
40×flip3-+ add-cbrt-cube flip-+
37×div-inv
24×cbrt-div
20×prod-exp cbrt-unprod
6×pow1
4×add-log-exp
3×pow1/3
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 861
Calls
4 calls:
835.0ms
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
64.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify338.0ms

Algorithm
egg-herbie
Counts
873 → 873
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500140817

prune3.6s

Filtered
873 candidates to 664 candidates (76.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes69.0ms

Accuracy

45.4% (1.3b remaining)

Error of 2.3b against oracle of 1.0b and baseline of 3.4b

bsearch72.0ms

Steps
ItersRangePoint
9
1.22827826888528e+120
2.4605251711493492e+126
2.3222667041145293e+126

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04335
14335

end0.0ms

sample514.0ms

Algorithm
intervals
Results
285.0ms8000×body80valid
90.0ms8000×pre80true