Details

Time bar (total: 3.1m)

sample73.0ms

Algorithm
intervals
Results
21.0ms15×body1280valid
19.0ms202×body80valid
8.0ms256×pre80true
8.0ms22×body640valid
3.0ms12×body320valid
1.0ms5×body160valid

simplify493.0ms

Calls
1 calls:
Slowest
492.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize36.0ms

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))

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- insert-posit16 flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Calls
3 calls:
Slowest
562.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
166.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
62.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series807.0ms

Calls
3 calls:
Slowest
370.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
319.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
118.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify26.1s

Calls
128 calls:
Slowest
788.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
739.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
711.0ms
(- (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))) (* 4.0 (/ 1 (pow alpha 2))))
616.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
604.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.9b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite568.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l* insert-posit16
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Calls
4 calls:
Slowest
296.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
138.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
86.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
39.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series888.0ms

Calls
4 calls:
Slowest
326.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
243.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
211.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
108.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.1m

Calls
368 calls:
Slowest
1.0s
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
1.0s
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
992.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
911.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
713.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize59.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
3.2b
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
1.9b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
0.1b
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
151×*-un-lft-identity
116×add-sqr-sqrt
90×associate-*r*
75×add-cube-cbrt
22×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×add-cbrt-cube add-exp-log
12×associate-/r/
9×flip3-+ flip-+
7×pow1
6×div-inv add-log-exp
5×associate-/l*
4×cbrt-undiv log-prod div-exp associate-*l* log-pow insert-posit16
3×exp-prod associate-/r* prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/ associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-- div-sub rem-log-exp exp-sum pow-prod-down associate-*r/ *-commutative flip--
Calls
4 calls:
Slowest
239.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
49.0ms
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))
19.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
13.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))

series1.3s

Calls
4 calls:
Slowest
414.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
412.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
337.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
113.0ms
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))

simplify35.1s

Calls
175 calls:
Slowest
1.4s
(* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (/ (* (* (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (* (* (+ 2.0 (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
928.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))
708.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
687.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
672.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize64.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))))))
3.2b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
3.2b
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
1.9b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
135×*-un-lft-identity
100×add-sqr-sqrt
90×associate-*r*
67×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
11×log-prod
10×associate-/r/
9×pow1 log-pow
8×flip3-+ flip-+
6×exp-prod add-log-exp
5×div-inv
4×associate-*l* insert-posit16
3×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
2×frac-times rem-log-exp associate-*l/
1×+-commutative sum-log exp-sum pow-prod-down associate-*r/ *-commutative
Calls
4 calls:
Slowest
333.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
14.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
10.0ms
(log (log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))))))
8.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))

series1.5s

Calls
4 calls:
Slowest
409.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
392.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
383.0ms
(log (log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))))))
349.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))

simplify35.7s

Calls
140 calls:
Slowest
1.0s
(* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (/ (* (* (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (* (* (+ 2.0 (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
742.0ms
(- (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))) (* 4.0 (/ 1 (pow alpha 2))))
742.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))
701.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
695.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

regimes355.0ms

Accuracy

6.1% (7.5b remaining)

Error of 11.6b against oracle of 4.1b and baseline of 12.1b

bsearch77.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s6392×body80valid
844.0ms558×body640valid
463.0ms8000×pre80true
431.0ms530×body1280valid
183.0ms335×body320valid
90.0ms185×body160valid