Details

Time bar (total: 18.7s)

sample53.0ms

Algorithm
intervals
Results
13.0ms208×body80valid
6.0ms256×pre80true
5.0ms15×body1280valid
4.0ms15×body640valid
2.0ms13×body320valid
1.0ms5×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
42747
3478
2106
131
015

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
0.0b
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
11.4b
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
166×times-frac
156×*-un-lft-identity
116×add-sqr-sqrt
78×add-cube-cbrt
24×associate-/l*
20×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
10×add-cbrt-cube add-exp-log
7×associate-/r* div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 div-sub log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg associate-/r/
1×flip3-+ flip3-- flip-+ fma-udef flip--
Counts
3 → 169
Calls
3 calls:
17.0ms
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
22.0ms
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
0.0ms
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series520.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
223.0ms
(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
211.0ms
(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify1.2s

Counts
178 → 178
Iterations
IterNodes
done5000
22673
1620
0250

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (- beta alpha))
11.4b
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
3.0ms
(cbrt (- beta alpha))
4.0ms
(cbrt (- beta alpha))
10.0ms
(cbrt (- beta alpha))
0.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

series933.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(cbrt (- beta alpha))
196.0ms
(cbrt (- beta alpha))
248.0ms
(cbrt (- beta alpha))
266.0ms
(fma (* (* (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha)))) (/ (cbrt (- beta alpha)) (cbrt (fma i 2.0 (+ beta alpha))))) (/ (/ (cbrt (- beta alpha)) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (cbrt (fma i 2.0 (+ beta alpha))))) (+ beta alpha) 1.0)

simplify2.0s

Counts
73 → 73
Iterations
IterNodes
done5000
34097
2781
1234
0106

prune805.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
0.0b
(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
0.1b
(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
2.3b
(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

rewrite159.0ms

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-+ 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 → 163
Calls
4 calls:
13.0ms
(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
18.0ms
(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
100.0ms
(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
22.0ms
(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (- beta alpha) (fma i 2.0 (+ beta alpha)))
122.0ms
(/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha))))
757.0ms
(* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha))))
290.0ms
(+ (* (/ (+ beta alpha) (+ 2.0 (fma i 2.0 (+ beta alpha)))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

simplify1.7s

Counts
175 → 175
Iterations
IterNodes
done5000
24167
1716
0242

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))))
0.4b
(/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
0.4b
(/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
7.4b
(+ (* (* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
106×times-frac
96×*-un-lft-identity
64×add-cube-cbrt
59×sqrt-prod
32×add-exp-log
28×associate-*r*
22×associate-*l*
20×add-cbrt-cube
15×unswap-sqr
13×distribute-lft-out
12×associate-/r*
11×div-exp
8×pow1 prod-exp
7×associate-/l*
6×cbrt-undiv add-log-exp
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp pow-flip
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×frac-times +-commutative sum-log fma-def sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow
Counts
4 → 202
Calls
4 calls:
52.0ms
(* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))))
32.0ms
(/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
11.0ms
(/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
109.0ms
(+ (* (* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

series791.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))))
234.0ms
(/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
140.0ms
(/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))
157.0ms
(+ (* (* (/ 1 (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0)))) (/ (+ alpha beta) (sqrt (fma i 2.0 (+ (+ alpha beta) 2.0))))) (/ (- beta alpha) (fma i 2.0 (+ beta alpha)))) 1.0)

simplify510.0ms

Counts
214 → 214
Iterations
IterNodes
done5001
1787
0269

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.1b

regimes384.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done21
121
018

end0.0ms

sample2.4s

Algorithm
intervals
Results
735.0ms6316×body80valid
717.0ms519×body1280valid
291.0ms582×body640valid
215.0ms8000×pre80true
96.0ms385×body320valid
35.0ms198×body160valid