Details

Time bar (total: 17.6s)

sample34.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
4.0ms256×pre80true

simplify93.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
34.0ms
(+ (+ alpha beta) (* beta alpha))
535.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
708.0ms
(/ (/ (/ (+ (+ (+ 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))
421.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ alpha beta) (* beta alpha))
196.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
221.0ms
(/ (/ (/ (+ (+ (+ 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))
100.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify125.0ms

Counts
475 → 475

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
444×times-frac
384×sqrt-prod
336×*-un-lft-identity
236×add-sqr-sqrt add-cube-cbrt
50×distribute-lft-out associate-/l*
36×associate-/r/
20×flip3-+ flip-+
18×associate-/r* div-inv
12×add-exp-log add-cbrt-cube
6×sqrt-div associate-/l/
4×pow1 cbrt-undiv frac-2neg div-exp clear-num add-log-exp
2×sqrt-undiv
Counts
4 → 408
Calls
4 calls:
379.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
380.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
378.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
452.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series830.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
262.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
132.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Counts
420 → 420

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite533.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
17×*-un-lft-identity
12×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt
10×flip3-+ flip-+
9×add-exp-log
8×associate-/l/
7×add-cbrt-cube
6×times-frac associate-/r* sqrt-prod
4×pow1 frac-times add-log-exp
3×pow1/3 distribute-lft-out
2×cbrt-undiv sqrt-div associate-*r/ div-exp associate-*l/ associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
278.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
90.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
69.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
90.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series628.0ms

Counts
4 → 12
Calls
4 calls:
342.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
100.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
98.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
88.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify46.0ms

Counts
91 → 91

prune576.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
603×times-frac
424×*-un-lft-identity
375×add-sqr-sqrt
279×cbrt-prod
244×add-cube-cbrt
194×associate-*l*
114×associate-*r*
90×distribute-lft-out
40×add-exp-log
28×add-cbrt-cube unswap-sqr
25×associate-/r/
20×cbrt-div
18×cbrt-undiv div-exp
15×flip3-+ flip-+
13×div-inv
9×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 → 408
Calls
4 calls:
2.1s
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
94.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
95.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
484.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series487.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
83.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
103.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
87.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify167.0ms

Counts
420 → 420

prune2.2s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.9b

regimes124.0ms

Accuracy

88.4% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 3.6b

bsearch7.0ms

simplify103.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
698.0ms8000×body80valid
338.0ms8000×pre80true