Details

Time bar (total: 1.3m)

sample75.0ms

Algorithm
intervals
Results
28.0ms200×body80valid
12.0ms24×body1280valid
9.0ms256×pre80true
6.0ms16×body640valid
3.0ms9×body320valid
1.0ms7×body160valid

simplify153.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize30.0ms

Local error

Found 4 expressions with local error:

20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.0b
(+ (/ (/ (* (+ 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))
0.0b
(* (+ alpha beta) (- beta alpha))

rewrite847.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity times-frac
62×add-sqr-sqrt
58×add-cube-cbrt
42×fma-def
24×associate-/r/
21×distribute-lft-out
20×add-cbrt-cube add-exp-log
19×flip3-+ flip-+
18×prod-diff
12×div-inv
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv associate-/r* div-exp
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*l* associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×clear-num sub-neg frac-2neg
1×+-commutative sum-log pow-prod-down *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 216
Calls
4 calls:
Slowest
564.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
186.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
47.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
41.0ms
(* (+ alpha beta) (- beta alpha))

series992.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
425.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
381.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
126.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
61.0ms
(* (+ alpha beta) (- beta alpha))

simplify41.1s

Counts
218 → 228
Calls
218 calls:
Slowest
758.0ms
(* (+ (pow alpha 3) (pow beta 3)) (- (* beta beta) (* alpha alpha)))
739.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
722.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
715.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
703.0ms
(/ (sqrt (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) 1)

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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--
Counts
4 → 115
Calls
4 calls:
Slowest
32.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
28.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
10.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
1.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series634.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(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)
132.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
90.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

simplify9.1s

Counts
107 → 127
Calls
107 calls:
Slowest
480.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
297.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
293.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
288.0ms
(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)))))
280.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
12×log-pow
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 sqrt-pow1 sqrt-prod
6×exp-prod add-exp-log
4×expm1-log1p-u add-cbrt-cube fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×pow1/2 rem-log-exp exp-sum
Counts
4 → 70
Calls
4 calls:
Slowest
6.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
6.0ms
(log (sqrt (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)
0.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
362.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
231.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
199.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify7.0s

Counts
36 → 82
Calls
36 calls:
Slowest
317.0ms
(log (sqrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
308.0ms
(log (sqrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
298.0ms
(sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
284.0ms
(log (sqrt (* (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))))))
279.0ms
(log (* (cbrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))) (cbrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
12×log-pow
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 sqrt-pow1 sqrt-prod
6×exp-prod add-exp-log
4×expm1-log1p-u add-cbrt-cube fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×pow1/2 rem-log-exp exp-sum
Counts
4 → 70
Calls
4 calls:
Slowest
3.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
3.0ms
(log (sqrt (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)
0.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
770.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
388.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
204.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
185.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify6.9s

Counts
36 → 82
Calls
36 calls:
Slowest
306.0ms
(log (sqrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
294.0ms
(sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
294.0ms
(sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
289.0ms
(log (sqrt (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
283.0ms
(log (sqrt (* (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))))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

regimes399.0ms

Accuracy

-7.5% (6.7b remaining)

Error of 12.1b against oracle of 5.4b and baseline of 11.6b

bsearch372.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s6452×body80valid
497.0ms8000×pre80true
418.0ms540×body640valid
400.0ms473×body1280valid
184.0ms355×body320valid
52.0ms180×body160valid