Details

Time bar (total: 25.2s)

sample140.0ms

Algorithm
intervals
Results
36.0ms199×body80valid
20.0ms21×body1280valid
18.0ms23×body640valid
14.0ms256×pre80true
6.0ms11×body320valid
1.0ms2×body160valid

simplify725.0ms

Counts
1 → 1

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize46.0ms

Local error

Found 3 expressions with local error:

1.2b
(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)))

rewrite41.0ms

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
21.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
18.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series408.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
201.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
112.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
95.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify1.5s

Counts
104 → 104

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize42.0ms

Local error

Found 4 expressions with local error:

3.6b
(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))))

rewrite101.0ms

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
50.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
31.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
16.0ms
(/ 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)

series636.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(fma (* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
139.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
135.0ms
(* (+ beta alpha) (/ 1 (+ 2.0 (fma 2 i (+ beta alpha)))))
104.0ms
(/ 1 (+ 2.0 (fma 2 i (+ beta alpha))))

simplify641.0ms

Counts
153 → 153

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
68×add-sqr-sqrt
66×times-frac
42×add-cube-cbrt
22×associate-*l*
20×add-cbrt-cube add-exp-log
19×associate-*r*
18×distribute-lft-out
9×associate-/l*
7×associate-/r* distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u flip3-+ prod-exp associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv unswap-sqr associate-/l/
2×clear-num frac-2neg
1×frac-times +-commutative sum-log fma-def flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 167
Calls
4 calls:
Slowest
67.0ms
(* (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
34.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
23.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
22.0ms
(+ (* (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) 1.0)

series829.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(* (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
259.0ms
(+ (* (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) 1.0)
133.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
97.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify1.0s

Counts
179 → 179

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
78×add-sqr-sqrt
70×times-frac
44×associate-*r*
42×add-cube-cbrt
38×associate-*l*
28×add-cbrt-cube add-exp-log
16×distribute-lft-out
8×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×distribute-lft-out-- add-log-exp difference-of-squares
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u div-inv
3×fma-neg prod-diff
2×frac-times flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
1×sub-neg flip3-- diff-log fma-udef flip--
Counts
4 → 168
Calls
4 calls:
Slowest
81.0ms
(* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))))
55.0ms
(* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))))
9.0ms
(- 1.0 (* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta))))))
0.0ms
(fma (* 1.0 1.0) 1.0 (* (* (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta)))) (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta))))) (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta))))))

series5.1s

Counts
4 → 12
Calls
4 calls:
Slowest
4.0s
(fma (* 1.0 1.0) 1.0 (* (* (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta)))) (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta))))) (* (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (fma 2 i (+ alpha beta))))))
410.0ms
(- 1.0 (* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta))))))
353.0ms
(* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))))
340.0ms
(* (/ (- beta alpha) (fma 2 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2 i (+ alpha beta)))))

simplify934.0ms

Counts
180 → 180

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.0b

regimes254.0ms

Accuracy

11.1% (5.6b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 12.1b

bsearch145.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s6384×body80valid
442.0ms8000×pre80true
439.0ms537×body1280valid
351.0ms562×body640valid
142.0ms346×body320valid
48.0ms171×body160valid