Details

Time bar (total: 9.7m)

sample58.0ms

Algorithm
intervals
Results
37.0ms256×body80valid
8.0ms256×pre80true

simplify150.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
149.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize34.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (* alpha beta) (+ beta alpha))

rewrite833.0ms

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×distribute-lft-out
778×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1217
Calls
4 calls:
Slowest
338.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
237.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
178.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
20.0ms
(+ (* alpha beta) (+ beta alpha))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
174.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
110.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
29.0ms
(+ (* alpha beta) (+ beta alpha))

simplify6.9m

Counts
2146 → 1229
Calls
2146 calls:
Slowest
1.0s
(/ (/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
975.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
970.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
842.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
832.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))

prune13.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize69.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.1b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.4b
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.4b
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite452.0ms

Algorithm
rewrite-expression-head
Rules
194×*-un-lft-identity
160×sqrt-prod
112×times-frac
76×add-sqr-sqrt
74×add-cube-cbrt
68×distribute-lft-out
16×associate-/r*
14×associate-/l*
12×sqrt-div
8×add-cbrt-cube add-exp-log
6×pow1 flip3-+ flip-+
4×associate-/r/ insert-posit16 add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 212
Calls
4 calls:
Slowest
205.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
132.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
57.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
52.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
139.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
89.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
83.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify28.5s

Counts
294 → 224
Calls
294 calls:
Slowest
328.0ms
(sqrt (+ 2 (+ beta alpha)))
327.0ms
(/ (* (* (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
301.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
300.0ms
(/ (* (* (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
294.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize53.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.2b
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.2b
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite875.0ms

Algorithm
rewrite-expression-head
Rules
1258×*-un-lft-identity
864×times-frac
768×sqrt-prod
528×distribute-lft-out
344×add-sqr-sqrt add-cube-cbrt
66×associate-/l*
44×associate-/r/
26×associate-/r*
24×flip3-+ flip-+
22×div-inv
12×add-cbrt-cube add-exp-log
6×sqrt-div associate-/l/
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 add-log-exp
2×sqrt-undiv
Counts
4 → 664
Calls
4 calls:
Slowest
230.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
211.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
210.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
187.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

series818.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
289.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
283.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
124.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
121.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.5m

Counts
1130 → 676
Calls
1130 calls:
Slowest
585.0ms
(/ (sqrt (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))))) (sqrt (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))))
552.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
498.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
430.0ms
(/ (* (* (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
352.0ms
(/ (sqrt (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha))))

prune7.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize64.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite489.0ms

Algorithm
rewrite-expression-head
Rules
196×*-un-lft-identity
84×distribute-lft-out
80×times-frac
48×add-sqr-sqrt add-cube-cbrt
20×associate-/r*
16×associate-/l*
12×add-cbrt-cube add-exp-log
8×flip3-+ associate-/r/ flip-+ associate-/l/
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
4 → 184
Calls
4 calls:
Slowest
123.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
122.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
121.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
119.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
85.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
84.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
82.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify14.9s

Counts
224 → 196
Calls
224 calls:
Slowest
348.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
345.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
344.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
343.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
340.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))))

prune2.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes90.0ms

Accuracy

53% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch73.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
919.0ms8000×body80valid
194.0ms8000×pre80true