Details

Time bar (total: 1.3m)

sample96.0ms

Algorithm
intervals
Results
31.0ms202×body80valid
15.0ms22×body640valid
13.0ms256×pre80true
12.0ms15×body1280valid
6.0ms12×body320valid
2.0ms5×body160valid

simplify153.0ms

Calls
1 calls:
Slowest
153.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize28.0ms

Local error

Found 3 expressions with local error:

19.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite770.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-cbrt-cube add-exp-log
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
5×add-log-exp
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Calls
3 calls:
Slowest
551.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
167.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
48.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series819.0ms

Calls
3 calls:
Slowest
415.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
301.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
103.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.9s

Calls
169 calls:
Slowest
765.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
753.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
729.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
707.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
662.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize57.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
1.5b
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0b
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
36×add-sqr-sqrt
32×times-frac
26×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
8×add-cbrt-cube add-exp-log
7×associate-/r*
5×pow1 distribute-lft-out-- difference-of-squares
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×exp-prod
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ fma-udef div-inv
1×flip3-- div-sub rem-log-exp exp-sum flip--
Calls
4 calls:
Slowest
16.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
13.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
2.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series679.0ms

Calls
4 calls:
Slowest
228.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
203.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
129.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
119.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

simplify9.4s

Calls
107 calls:
Slowest
474.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
341.0ms
(log (* (cbrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))) (cbrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
285.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
280.0ms
(sqrt (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))
268.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize48.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
1.5b
(log (exp (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))
0.1b
(* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))))
0.0b
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
53×add-sqr-sqrt
48×times-frac
33×add-cube-cbrt
26×associate-*l*
18×add-cbrt-cube add-exp-log
16×associate-*r*
12×distribute-lft-out
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u log-prod prod-exp log-pow cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
3×exp-prod associate-/r* flip3-+ flip-+ div-inv
2×associate-/r/ associate-/l/
1×frac-times +-commutative clear-num sum-log fma-def frac-2neg rem-log-exp exp-sum pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
4 calls:
Slowest
52.0ms
(log (exp (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))
35.0ms
(* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))))
21.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
14.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

series876.0ms

Calls
4 calls:
Slowest
287.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
277.0ms
(* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))))
224.0ms
(log (exp (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))
87.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

simplify12.5s

Calls
117 calls:
Slowest
866.0ms
(* (* (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha)))))
769.0ms
(* (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha)))))
490.0ms
(* (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) (* (* (/ (+ beta alpha) (fma 2 i (+ beta alpha))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))))
429.0ms
(/ (- beta alpha) (+ (pow 2.0 3) (pow (fma 2 i (+ beta alpha)) 3)))
389.0ms
(+ (- (log (- beta alpha)) (log (+ 2.0 (fma 2 i (+ beta alpha))))) (- (log (+ beta alpha)) (log (fma 2 i (+ beta alpha)))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 log-pow
4×expm1-log1p-u exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×+-commutative log-prod sum-log fma-def flip3-+ flip-+
1×cbrt-prod rem-log-exp
Calls
4 calls:
Slowest
31.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
20.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
19.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
5.0ms
(log (exp (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))))

series923.0ms

Calls
4 calls:
Slowest
242.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
234.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
232.0ms
(log (exp (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))))
214.0ms
(+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)

simplify5.7s

Calls
26 calls:
Slowest
345.0ms
(cbrt (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0))))
344.0ms
(log (* (cbrt (exp (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0))))) (cbrt (exp (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))))))
335.0ms
(cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)))
311.0ms
(sqrt (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0))))
309.0ms
(log (sqrt (exp (cbrt (* (* (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0)) (+ (* (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha)))) 1.0))))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

regimes472.0ms

Accuracy

8.6% (5.7b remaining)

Error of 11.6b against oracle of 5.8b and baseline of 12.1b

bsearch54.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
994.0ms6392×body80valid
848.0ms530×body1280valid
399.0ms558×body640valid
385.0ms8000×pre80true
168.0ms335×body320valid
49.0ms185×body160valid