Details

Time bar (total: 4.7m)

sample41.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
7.0ms256×pre80true

simplify128.0ms

Calls
1 calls:
Slowest
128.0ms
(/ (/ (/ (+ (+ (+ 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: 4.8b

localize32.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
257×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-/l*
46×associate-/r/
25×flip3-+ flip-+
23×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num fma-def frac-2neg
1×+-commutative associate-+l+
Calls
4 calls:
Slowest
24.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
21.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
7.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
7.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series528.0ms

Calls
4 calls:
Slowest
204.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
184.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
122.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
17.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.9m

Calls
525 calls:
Slowest
929.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
920.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
773.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
773.0ms
(/ (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
767.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize11.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ 2 (+ 1.0 (+ beta alpha)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
256×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-/l*
46×associate-/r/
25×flip3-+ flip-+
23×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+r+
Calls
4 calls:
Slowest
32.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
27.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
3.0ms
(+ 2 (+ 1.0 (+ beta alpha)))

series540.0ms

Calls
4 calls:
Slowest
231.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
169.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
125.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
14.0ms
(+ 2 (+ 1.0 (+ beta alpha)))

simplify1.8m

Calls
524 calls:
Slowest
765.0ms
(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
717.0ms
(/ (/ (cbrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
692.0ms
(/ (* (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (+ 2 (+ 1.0 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))) (+ 2 (+ 1.0 (+ beta alpha)))))
681.0ms
(/ (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))
613.0ms
(/ (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))

prune4.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize27.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
90×sqrt-prod
72×times-frac
64×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
12×associate-/r* sqrt-div associate-/l*
8×add-cbrt-cube add-exp-log
6×flip3-+ flip-+
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
12.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
11.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
2.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series448.0ms

Calls
4 calls:
Slowest
155.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
137.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
85.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
71.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify23.9s

Calls
204 calls:
Slowest
367.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
347.0ms
(sqrt (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
338.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
304.0ms
(sqrt (+ (pow 1.0 3) (pow (fma beta alpha (+ beta alpha)) 3)))
295.0ms
(sqrt (- (* 1.0 1.0) (* (fma beta alpha (+ beta alpha)) (fma beta alpha (+ beta alpha)))))

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize27.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (+ 2 (+ beta alpha)) (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
39×times-frac
38×add-sqr-sqrt
36×*-un-lft-identity add-cube-cbrt
14×add-exp-log
12×sqrt-div
11×add-cbrt-cube
9×associate-/l*
8×associate-/r/
7×associate-/r* flip3-+ flip-+
4×expm1-log1p-u pow1 div-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×cbrt-undiv
2×frac-times rem-sqrt-square clear-num frac-2neg pow1/2 associate-*l/ prod-exp div-inv
1×rec-exp sqrt-undiv associate-*r/ un-div-inv cbrt-unprod
Calls
4 calls:
Slowest
18.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
11.0ms
(/ (+ 2 (+ beta alpha)) (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha))))))
2.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series815.0ms

Calls
4 calls:
Slowest
545.0ms
(/ (+ 2 (+ beta alpha)) (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha))))))
129.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
80.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
60.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify17.9s

Calls
136 calls:
Slowest
603.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))
483.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (* (* (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (* (* (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha))))) (/ 1 (sqrt (+ 2 (+ beta alpha)))))))
479.0ms
(/ (sqrt 1) (* (cbrt (sqrt (+ 2 (+ beta alpha)))) (cbrt (sqrt (+ 2 (+ beta alpha))))))
455.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (* (* (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha))))) (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha)))))) (* (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (/ 1 (sqrt (+ 2 (+ beta alpha)))))))
442.0ms
(* (sqrt (+ (* 1.0 1.0) (- (* (fma beta alpha (+ beta alpha)) (fma beta alpha (+ beta alpha))) (* 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (+ 2 (+ beta alpha))))

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

regimes117.0ms

Accuracy

52.9% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.4b

bsearch39.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
385.0ms8000×pre80true