Details

Time bar (total: 2.9m)

sample92.0ms

Algorithm
intervals
Results
27.0ms200×body80valid
12.0ms256×pre80true
11.0ms16×body1280valid
11.0ms21×body640valid
6.0ms15×body320valid
1.0ms4×body160valid

simplify129.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
128.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize34.0ms

Local error

Found 3 expressions with local error:

23.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite935.0ms

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
Counts
3 → 162
Calls
3 calls:
Slowest
653.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
197.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series834.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
359.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
340.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
135.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.6s

Counts
169 → 171
Calls
169 calls:
Slowest
803.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
723.0ms
(* (- (* alpha alpha) (* beta beta)) (- (* beta beta) (* alpha alpha)))
712.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
707.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
701.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
0.1b
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
0.0b
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×associate-*r*
7×associate-/r* distribute-lft-out-- difference-of-squares associate-/l/
6×pow1 cbrt-undiv flip3-+ div-exp flip-+ associate-/l* add-log-exp
4×expm1-log1p-u frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out
3×div-inv
2×clear-num frac-2neg associate-*r/ associate-/r/ unswap-sqr
1×+-commutative sum-log fma-def flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 138
Calls
4 calls:
Slowest
52.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
41.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
26.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
20.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))

series855.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
257.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
117.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
110.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify13.7s

Counts
118 → 150
Calls
118 calls:
Slowest
797.0ms
(/ (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
711.0ms
(/ (* (* (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
682.0ms
(/ (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (/ (- beta alpha) (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
582.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))
563.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

8.9b
(+ (* 1 (* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))) 1.0)
0.4b
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
0.4b
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
0.3b
(* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
575×times-frac
469×*-un-lft-identity
400×add-sqr-sqrt
252×add-cube-cbrt
203×sqrt-prod
139×associate-*r*
64×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
34×associate-*l*
32×add-cbrt-cube add-exp-log
23×associate-/l*
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div associate-/r/
6×pow1 flip3-+ prod-exp cbrt-unprod flip-+ add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/l/
2×clear-num frac-2neg div-sub
1×frac-times +-commutative sum-log fma-def pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 469
Calls
4 calls:
Slowest
97.0ms
(+ (* 1 (* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))) 1.0)
79.0ms
(* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))
30.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
18.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
326.0ms
(* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))
281.0ms
(+ (* 1 (* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))))) 1.0)
230.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))

simplify1.4m

Counts
603 → 481
Calls
603 calls:
Slowest
894.0ms
(* (/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 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)))) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))))
840.0ms
(sqrt (+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha))))))
744.0ms
(* (/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 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)))) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))))
710.0ms
(* (* (* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (+ beta alpha) (sqrt (+ 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)))) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))))
569.0ms
(* (* (* (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (+ beta alpha) (sqrt (+ 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)))) (* (* (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))))

prune7.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))) 1.0)
0.1b
(* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta)))))
0.0b
(/ (- beta alpha) (fma i 2 (+ alpha beta)))
0.0b
(/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
68×add-sqr-sqrt
66×times-frac
42×add-cube-cbrt
22×associate-*r*
20×add-cbrt-cube add-exp-log
19×associate-*l*
18×distribute-lft-out
9×associate-/l*
7×associate-/r* distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u flip3-+ prod-exp associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv unswap-sqr associate-/l/
2×clear-num frac-2neg
1×frac-times +-commutative sum-log fma-def flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 167
Calls
4 calls:
Slowest
51.0ms
(* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta)))))
28.0ms
(+ (* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))) 1.0)
26.0ms
(/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))
24.0ms
(/ (- beta alpha) (fma i 2 (+ alpha beta)))

series778.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta)))))
242.0ms
(+ (* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))) 1.0)
115.0ms
(/ (- beta alpha) (fma i 2 (+ alpha beta)))
93.0ms
(/ (+ alpha beta) (+ 2.0 (fma i 2 (+ alpha beta))))

simplify15.4s

Counts
160 → 179
Calls
160 calls:
Slowest
712.0ms
(* (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))) (fma i 2 (+ alpha beta)))) (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (+ 2.0 (fma i 2 (+ alpha beta))) (+ 2.0 (fma i 2 (+ alpha beta)))) (+ 2.0 (fma i 2 (+ alpha beta))))))
528.0ms
(* (* (* (/ (- beta alpha) (fma i 2 (+ alpha beta))) (/ (- beta alpha) (fma i 2 (+ alpha beta)))) (/ (- beta alpha) (fma i 2 (+ alpha beta)))) (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (+ 2.0 (fma i 2 (+ alpha beta))) (+ 2.0 (fma i 2 (+ alpha beta)))) (+ 2.0 (fma i 2 (+ alpha beta))))))
513.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))) (fma i 2 (+ alpha beta))))
478.0ms
(+ (- (log (- beta alpha)) (log (fma i 2 (+ alpha beta)))) (- (log (+ alpha beta)) (log (+ 2.0 (fma i 2 (+ alpha beta))))))
475.0ms
(+ (* 2.0 2.0) (- (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))) (* 2.0 (fma i 2 (+ alpha beta)))))

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.0b

regimes540.0ms

Accuracy

-7.8% (6.6b remaining)

Error of 12.3b against oracle of 5.7b and baseline of 11.9b

bsearch286.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.2s6435×body80valid
852.0ms467×body1280valid
489.0ms575×body640valid
405.0ms8000×pre80true
167.0ms351×body320valid
85.0ms172×body160valid