Details

Time bar (total: 7.4m)

sample72.0ms

Algorithm
intervals
Results
23.0ms202×body80valid
12.0ms22×body1280valid
10.0ms256×pre80true
9.0ms19×body640valid
2.0ms7×body320valid
1.0ms6×body160valid

simplify121.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
121.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize36.0ms

Local error

Found 4 expressions with local error:

23.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.2b
(+ (/ (/ (* (+ 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))
0.0b
(+ (+ alpha beta) (* 2 i))

rewrite836.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
46×fma-def
45×add-sqr-sqrt add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
12×div-inv
11×add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
4×expm1-log1p-u frac-times pow1 sum-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 182
Calls
4 calls:
Slowest
549.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
178.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
63.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
43.0ms
(+ (+ alpha beta) (* 2 i))

series891.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
424.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
324.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
122.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
22.0ms
(+ (+ alpha beta) (* 2 i))

simplify34.3s

Counts
176 → 194
Calls
176 calls:
Slowest
1.1s
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
809.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
766.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
704.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
664.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize37.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
1.2b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
2182×times-frac
1819×*-un-lft-identity
1037×add-sqr-sqrt
783×add-cube-cbrt
391×distribute-lft-out
361×fma-def
127×distribute-lft-out-- difference-of-squares
113×associate-/r*
96×associate-/r/
54×div-inv
45×flip3-+ flip-+
20×add-cbrt-cube add-exp-log
13×associate-/l*
10×cbrt-undiv div-exp
6×add-log-exp associate-/l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
1×+-commutative sum-log flip3-- div-sub flip--
Counts
4 → 1019
Calls
4 calls:
Slowest
626.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
266.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
210.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
42.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
262.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
236.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
108.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify4.9m

Counts
1427 → 1031
Calls
1427 calls:
Slowest
935.0ms
(/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
900.0ms
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
883.0ms
(/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
755.0ms
(- (+ (* 8 (/ (* i beta) alpha)) (+ (* 4 (/ (* (pow i 2) beta) (pow alpha 2))) (* 4 (/ (pow i 2) alpha)))))
724.0ms
(/ (+ beta alpha) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

prune14.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize44.0ms

Local error

Found 4 expressions with local error:

12.8b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(+ (+ alpha beta) (* 2 i))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
166×*-un-lft-identity
120×add-sqr-sqrt
82×add-cube-cbrt
26×associate-/l*
23×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
11×add-cbrt-cube add-exp-log
9×add-log-exp
8×flip3-+ flip-+
7×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv fma-def div-exp insert-posit16 log1p-expm1-u
3×sum-log div-sub associate-/l/
2×clear-num frac-2neg
1×+-commutative associate-+l+ flip3-- fma-udef flip--
Counts
4 → 204
Calls
4 calls:
Slowest
182.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
35.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
27.0ms
(+ (+ alpha beta) (* 2 i))
0.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
214.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
112.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
35.0ms
(+ (+ alpha beta) (* 2 i))

simplify42.4s

Counts
259 → 216
Calls
259 calls:
Slowest
1.2s
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
894.0ms
(/ (/ (* (* (- 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)))
867.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
767.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
743.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

localize69.0ms

Local error

Found 4 expressions with local error:

12.8b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
2.6b
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
0.2b
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
148×*-un-lft-identity
104×add-sqr-sqrt
74×add-cube-cbrt
22×distribute-lft-out
21×associate-/l*
15×distribute-lft-out-- difference-of-squares
12×associate-/r/
10×add-exp-log
9×add-cbrt-cube
6×pow1 log-prod flip3-+ flip-+ div-inv
4×expm1-log1p-u exp-prod associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp exp-sum
2×div-sub log-pow
1×clear-num frac-2neg rem-log-exp fma-udef rem-exp-log associate-/l/
Counts
4 → 174
Calls
4 calls:
Slowest
154.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
5.0ms
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
2.0ms
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
1.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
241.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
214.0ms
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
213.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

simplify41.8s

Counts
224 → 186
Calls
224 calls:
Slowest
1.2s
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
875.0ms
(/ (/ (* (* (- 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)))
762.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
753.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
724.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.7b

regimes558.0ms

Accuracy

16.7% (5.4b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 12.3b

bsearch176.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.6s6369×body80valid
458.0ms535×body1280valid
424.0ms563×body640valid
408.0ms8000×pre80true
144.0ms327×body320valid
59.0ms206×body160valid