Details

Time bar (total: 36.2s)

sample113.0ms

Algorithm
intervals
Results
46.0ms212×body80valid
15.0ms256×pre80true
14.0ms19×body640valid
8.0ms9×body1280valid
6.0ms12×body320valid
1.0ms4×body160valid

simplify786.0ms

Counts
1 → 1

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize55.0ms

Local error

Found 3 expressions with local error:

0.7b
(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))))

rewrite48.0ms

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
23.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
23.0ms
(/ (+ 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)

series434.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
191.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
150.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
93.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify1.4s

Counts
104 → 104

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.1b

localize68.0ms

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)
0.1b
(* (+ 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))))

rewrite68.0ms

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
33.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
16.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
15.0ms
(/ 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)

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
138.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
111.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
79.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

simplify627.0ms

Counts
153 → 153

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (/ (/ (+ 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))

rewrite327.0ms

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
147.0ms
(+ (/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha))) 1.0)
58.0ms
(/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha)))
23.0ms
(/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0))
17.0ms
(/ (fma 2 i (+ alpha beta)) (- beta alpha))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
427.0ms
(+ (/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha))) 1.0)
366.0ms
(/ (/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0)) (/ (fma 2 i (+ alpha beta)) (- beta alpha)))
109.0ms
(/ (+ alpha beta) (+ (fma 2 i (+ alpha beta)) 2.0))
101.0ms
(/ (fma 2 i (+ alpha beta)) (- beta alpha))

simplify1.5s

Counts
1105 → 1105

prune17.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize54.0ms

Local error

Found 4 expressions with local error:

5.0b
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
5.0b
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
5.0b
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
0.7b
(fma (* (* (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
66×cbrt-prod
48×times-frac
31×add-sqr-sqrt add-cube-cbrt
24×distribute-lft-out
6×associate-/r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×fma-udef
Counts
4 → 113
Calls
4 calls:
Slowest
11.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
11.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
10.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
0.0ms
(fma (* (* (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
421.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
407.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
400.0ms
(cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
222.0ms
(fma (* (* (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (cbrt (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify1.1s

Counts
125 → 125

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes321.0ms

Accuracy

0% (6.4b remaining)

Error of 12.1b against oracle of 5.7b and baseline of 12.1b

bsearch3.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.7s6407×body80valid
393.0ms484×body1280valid
364.0ms8000×pre80true
350.0ms585×body640valid
200.0ms361×body320valid
114.0ms163×body160valid