Details

Time bar (total: 5.5m)

sample45.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
7.0ms256×pre80true

simplify115.0ms

Calls
1 calls:
Slowest
115.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize54.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 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)

rewrite81.0ms

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
40.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
16.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
12.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
5.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series226.0ms

Calls
4 calls:
Slowest
89.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
75.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
49.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
13.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.9m

Calls
525 calls:
Slowest
1.0s
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
824.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
781.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
741.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
705.0ms
(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize9.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
177×times-frac
103×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
71×associate-/r*
28×add-exp-log
25×associate-/r/
16×div-inv
14×div-exp
13×add-cbrt-cube
11×flip3-+ flip-+ associate-/l*
6×rec-exp
5×pow1 cbrt-undiv associate-/l/
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×pow-flip inv-pow
Calls
4 calls:
Slowest
18.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
10.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
9.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
6.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))

series356.0ms

Calls
4 calls:
Slowest
122.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
87.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
84.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
63.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify49.6s

Calls
250 calls:
Slowest
926.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
884.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
839.0ms
(/ (* (* (/ 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)))
809.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
665.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (* (* (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 1.0 (fma beta alpha (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
95×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
68×associate-/r*
39×add-exp-log
22×associate-/r/
13×rec-exp add-cbrt-cube div-exp div-inv
11×flip3-+ flip-+
9×pow1
8×prod-exp
6×associate-*r* associate-/l*
5×associate-*l*
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg pow-prod-down pow-flip inv-pow
1×frac-times associate-*l/ associate-*r/ un-div-inv *-commutative cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
15.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
7.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
6.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))

series344.0ms

Calls
4 calls:
Slowest
106.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
101.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
90.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
46.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify42.1s

Calls
234 calls:
Slowest
675.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (* (* (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 1.0 (fma beta alpha (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
595.0ms
(/ 1 (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
563.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))
517.0ms
(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))))
502.0ms
(sqrt (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0))
0.1b
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
0.0b
(/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta)))
0.0b
(+ (fma beta alpha (+ alpha beta)) 1.0)

rewrite86.0ms

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+ fma-udef
Calls
4 calls:
Slowest
32.0ms
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
29.0ms
(/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta)))
13.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0))
3.0ms
(+ (fma beta alpha (+ alpha beta)) 1.0)

series235.0ms

Calls
4 calls:
Slowest
92.0ms
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
83.0ms
(/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta)))
48.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0))
12.0ms
(+ (fma beta alpha (+ alpha beta)) 1.0)

simplify1.8m

Calls
526 calls:
Slowest
877.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (pow (+ 2 (+ alpha beta)) 3) (pow 1.0 3)))
803.0ms
(/ (/ (/ 1 (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))) (sqrt (+ 2 (+ alpha beta))))
797.0ms
(/ (/ (/ 1 (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))) (cbrt (+ 2 (+ alpha beta))))
782.0ms
(/ (* (cbrt (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta)))) (cbrt (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (+ 2 (+ alpha beta))))) (* (cbrt (+ 2 (+ alpha beta))) (cbrt (+ 2 (+ alpha beta)))))
649.0ms
(/ (/ (* (* (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0)) (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0))) (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (+ (+ 2 (+ alpha beta)) 1.0))) (* (* (+ 2 (+ alpha beta)) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))) (* (* (+ 2 (+ alpha beta)) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))))

prune4.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

68% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.5b

bsearch123.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s8000×body80valid
266.0ms8000×pre80true