Details

Time bar (total: 34.1s)

sample85.0ms

Algorithm
intervals
Results
27.0ms205×body80valid
12.0ms20×body1280valid
10.0ms256×pre80true
8.0ms16×body640valid
4.0ms9×body320valid
2.0ms6×body160valid

simplify924.0ms

Counts
1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize42.0ms

Local error

Found 3 expressions with local error:

1.9b
(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))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
31×add-sqr-sqrt times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×associate-/r* add-cbrt-cube add-exp-log
4×distribute-lft-out-- difference-of-squares associate-/l/
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ div-inv
1×flip3-- div-sub fma-udef flip--
Counts
3 → 95
Calls
3 calls:
Slowest
24.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
18.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
1.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series445.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
234.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
115.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
95.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify1.3s

Counts
104 → 104

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.9b

localize56.0ms

Local error

Found 4 expressions with local error:

2.4b
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.2b
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
47×add-sqr-sqrt
41×times-frac
32×add-cube-cbrt
19×add-exp-log
18×associate-*r*
13×add-cbrt-cube
8×distribute-lft-out associate-/l*
7×pow1 associate-/r*
5×div-exp
4×expm1-log1p-u flip3-+ associate-*l* prod-exp associate-/r/ flip-+ insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×cbrt-undiv div-inv unswap-sqr
2×frac-times rec-exp clear-num frac-2neg 1-exp associate-*l/ cbrt-unprod associate-/l/
1×flip3-- div-sub pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef pow-flip flip-- inv-pow
Counts
4 → 141
Calls
4 calls:
Slowest
51.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
31.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
8.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
1.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
201.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
136.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))
122.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
89.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify606.0ms

Counts
153 → 153

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.9b

localize79.0ms

Local error

Found 4 expressions with local error:

3.8b
(log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))))
2.4b
(fma (log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.2b
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
39×add-sqr-sqrt
29×times-frac
24×add-cube-cbrt
18×associate-*r*
15×add-exp-log
11×add-cbrt-cube
7×pow1 add-log-exp
5×associate-/l*
4×expm1-log1p-u associate-*l* prod-exp log-pow insert-posit16 log1p-expm1-u distribute-lft-out distribute-lft-out-- difference-of-squares
3×log-prod associate-/r* flip3-+ div-exp flip-+ unswap-sqr
2×frac-times cbrt-undiv exp-to-pow associate-*l/ associate-/r/ cbrt-unprod div-inv associate-/l/
1×rec-exp exp-prod clear-num sum-log frac-2neg flip3-- 1-exp div-sub rem-log-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef flip--
Counts
4 → 119
Calls
4 calls:
Slowest
26.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
23.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
7.0ms
(log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))))
0.0ms
(fma (log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series489.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(fma (log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
98.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
97.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
97.0ms
(log (exp (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))))

simplify633.0ms

Counts
131 → 131

prune2.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.9b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
2318×times-frac
1805×*-un-lft-identity
1095×add-sqr-sqrt
817×add-cube-cbrt
467×fma-def
355×distribute-lft-out
182×associate-/r/
139×distribute-lft-out-- difference-of-squares
92×div-inv
46×flip3-+ flip3-- flip-+ flip--
30×associate-/r*
29×associate-/l*
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg associate-/l/
1×+-commutative sum-log
Counts
4 → 1093
Calls
4 calls:
Slowest
86.0ms
(+ (/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha))) 1.0)
41.0ms
(/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha)))
25.0ms
(/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0))
16.0ms
(/ (fma 2 i (+ alpha beta)) (- beta alpha))

series869.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
380.0ms
(+ (/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha))) 1.0)
308.0ms
(/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha)))
103.0ms
(/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0))
78.0ms
(/ (fma 2 i (+ alpha beta)) (- beta alpha))

simplify1.4s

Counts
1105 → 1105

prune16.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

regimes408.0ms

Accuracy

15.8% (5.3b remaining)

Error of 11.4b against oracle of 6.1b and baseline of 12.4b

bsearch141.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s6357×body80valid
927.0ms522×body1280valid
490.0ms8000×pre80true
406.0ms547×body640valid
164.0ms365×body320valid
61.0ms209×body160valid