Details

Time bar (total: 10.0m)

sample117.0ms

Algorithm
intervals
Results
51.0ms210×body80valid
14.0ms256×pre80true
13.0ms19×body640valid
9.0ms12×body1280valid
5.0ms10×body320valid
2.0ms5×body160valid

simplify807.0ms

Counts
1 → 1
Iterations
IterNodes
42315
3458
299
132
016

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
1.5b
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
26.6b
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
8×associate-/l/
7×fma-def
6×times-frac add-log-exp
4×expm1-log1p-u frac-times flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- swap-sqr associate-*r* associate-*l* fma-udef flip--
2×cbrt-undiv div-exp associate-*l/ prod-exp associate-*r/ cbrt-unprod div-inv
1×pow2 distribute-rgt-in +-commutative clear-num sum-log frac-2neg distribute-lft-in pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up distribute-lft-out associate-/l* unswap-sqr
Counts
4 → 95
Calls
4 calls:
0.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
7.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
36.0ms
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
37.0ms
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series886.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
89.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
264.0ms
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
374.0ms
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify4.6s

Counts
107 → 107
Iterations
IterNodes
38699
21759
1493
0175

prune596.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
0.1b
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
1.5b
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
12.4b
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
143×*-un-lft-identity
131×frac-times
88×times-frac
85×add-sqr-sqrt
77×associate-*l/
65×associate-*r/
63×cbrt-div
52×associate-*r* associate-*l*
45×add-cube-cbrt distribute-lft-out
28×add-cbrt-cube add-exp-log
8×pow1 cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
6×add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u div-inv
2×cbrt-prod pow-prod-down *-commutative
1×+-commutative sum-log pow1/3 pow3 rem-cbrt-cube
Counts
4 → 253
Calls
4 calls:
83.0ms
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
105.0ms
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
15.0ms
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
847.0ms
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
307.0ms
(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
447.0ms
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
460.0ms
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

simplify2.4s

Counts
265 → 265
Iterations
IterNodes
24985
11152
0411

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

localize102.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (fma i 2 alpha) beta))
1.9b
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))) 1.0)
2.4b
(* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
12.4b
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
330×frac-times
182×associate-*r/
156×associate-*l/
155×add-exp-log
141×cbrt-div
78×prod-exp
57×add-cbrt-cube
48×div-exp
32×cbrt-unprod
22×cbrt-undiv
15×associate-*l*
12×*-un-lft-identity
10×rec-exp 1-exp
9×pow1
8×add-sqr-sqrt flip3-+ associate-/r/ add-cube-cbrt flip-+
6×cbrt-prod add-log-exp
4×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u
3×times-frac pow-prod-down
2×pow1/3 distribute-lft-out
1×+-commutative sum-log associate-*r* *-commutative div-inv
Counts
4 → 261
Calls
4 calls:
3.0ms
(cbrt (+ (fma i 2 alpha) beta))
30.0ms
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))) 1.0)
170.0ms
(* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
1.4s
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
274.0ms
(cbrt (+ (fma i 2 alpha) beta))
371.0ms
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))) 1.0)
408.0ms
(* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
441.0ms
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))))

simplify1.2s

Counts
273 → 273
Iterations
IterNodes
12069
0724

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.5b

localize120.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (fma i 2 alpha) beta))
1.9b
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (log1p (expm1 (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))))) 1.0)
2.4b
(* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
12.4b
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (log1p (expm1 (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))))))

rewrite893.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
78×prod-exp
57×add-cbrt-cube
48×div-exp
32×cbrt-unprod
31×associate-*l/
29×cbrt-div
26×frac-times
22×cbrt-undiv
18×associate-*r/
15×associate-*l*
12×*-un-lft-identity
10×rec-exp 1-exp
9×pow1
8×add-sqr-sqrt flip3-+ associate-/r/ add-cube-cbrt flip-+
6×cbrt-prod add-log-exp
4×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u
3×times-frac pow-prod-down
2×pow1/3 distribute-lft-out
1×+-commutative sum-log associate-*r* *-commutative div-inv
Counts
4 → 149
Calls
4 calls:
3.0ms
(cbrt (+ (fma i 2 alpha) beta))
14.0ms
(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (log1p (expm1 (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))))) 1.0)
173.0ms
(* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))
699.0ms
(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (log1p (expm1 (* (/ 1 (* (cbrt (+ (fma i 2 alpha) beta)) (cbrt (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (cbrt (+ (fma i 2 alpha) beta))) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))))))

series9.6m