Details

Time bar (total: 9.9m)

sample54.0ms

Algorithm
intervals
Results
32.0ms256×body80valid
8.0ms256×pre80true

simplify136.0ms

Calls
1 calls:
Slowest
135.0ms
(/ (/ (/ (+ (+ (+ 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: 5.8b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 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)

rewrite70.0ms

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
25.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
20.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
10.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
8.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series291.0ms

Calls
4 calls:
Slowest
121.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
104.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
51.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
14.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.9m

Calls
525 calls:
Slowest
832.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
753.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
750.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
745.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
742.0ms
(/ (/ (cbrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize22.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
0.1b
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.1b
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))
0.0b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
87×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×associate-/r/
29×associate-/l*
28×add-exp-log
25×div-inv
24×associate-/r*
14×div-exp
13×add-cbrt-cube
9×flip3-+ flip-+
6×rec-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×pow-flip inv-pow
Calls
4 calls:
Slowest
30.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
14.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
5.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))
2.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))

series282.0ms

Calls
4 calls:
Slowest
96.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
75.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))
60.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))
51.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify55.1s

Calls
258 calls:
Slowest
758.0ms
(+ (* 1.0 1.0) (- (* (fma beta alpha (+ beta alpha)) (fma beta alpha (+ beta alpha))) (* 1.0 (fma beta alpha (+ beta alpha)))))
679.0ms
(/ (* (* (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))) (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
625.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
581.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))
565.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
0.4b
(/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))
0.1b
(/ (/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
3660×times-frac
1412×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
915×sqrt-prod
365×associate-/r/
297×div-inv associate-/l*
229×sqrt-div
70×flip3-+ flip-+
27×associate-/r*
22×add-exp-log
17×add-cbrt-cube
11×div-exp
8×cbrt-undiv
5×pow1 associate-/l/
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp pow-flip
1×pow1/2 inv-pow
Calls
4 calls:
Slowest
53.0ms
(/ (/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
16.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
15.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
4.0ms
(/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))

series299.0ms

Calls
4 calls:
Slowest
104.0ms
(/ (/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
67.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
65.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
64.0ms
(/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))

simplify7.0m

Calls
2140 calls:
Slowest
799.0ms
(/ (/ (/ (sqrt (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))) (sqrt (/ (+ 2 (+ beta alpha)) (- (* 1.0 1.0) (* (fma beta alpha (+ beta alpha)) (fma beta alpha (+ beta alpha))))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
732.0ms
(/ (/ (* (cbrt (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))) (cbrt (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))))) 1) 1)
688.0ms
(/ (/ (cbrt (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
686.0ms
(/ (/ (sqrt (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
685.0ms
(/ (/ (/ (cbrt (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))))) (sqrt (/ (cbrt (+ 2 (+ beta alpha))) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (cbrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))