Details

Time bar (total: 11.7s)

sample29.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
5.0ms256×pre80true

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123
done500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
39.7b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
40.7b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite713.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
17×cbrt-undiv div-exp
16×add-cube-cbrt *-un-lft-identity times-frac
15×prod-exp cbrt-unprod
13×pow1
10×associate-/r*
8×associate-*l/
7×flip3-+ associate-*l* flip-+
6×associate-*r*
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u div-inv associate-/l/ add-log-exp
3×swap-sqr
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative flip-- fma-udef associate-/l* unswap-sqr
1×pow2 pow-plus associate-/r/ pow-sqr pow-prod-up difference-of-squares
Counts
4 → 135
Calls
4 calls:
138.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
185.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
217.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
167.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
271.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
2.0s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
820.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify53.0ms

Counts
147 → 147
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09113106
150022350
done50022350

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
3.5b
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
30.6b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
34.8b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
65×*-un-lft-identity
62×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
50×add-cube-cbrt
29×cbrt-undiv div-exp
19×associate-*r* associate-/r*
13×associate-*l*
12×prod-exp cbrt-unprod
9×distribute-lft-out
7×div-inv associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down associate-/r/ *-commutative
Counts
4 → 179
Calls
4 calls:
85.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
49.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
367.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
832.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
173.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
100.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify123.0ms

Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08383659
148932981
250012981
done50012981

prune604.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize23.0ms

Local error

Found 4 expressions with local error:

30.6b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
30.6b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
34.8b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
34.8b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
12×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
4 → 116
Calls
4 calls:
5.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
5.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series563.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
179.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
103.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
103.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify116.0ms

Counts
128 → 128
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
02201436
17311316
235281314
350021312
done50021312

prune601.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
3.5b
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
30.6b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
34.8b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
65×*-un-lft-identity
62×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
50×add-cube-cbrt
29×cbrt-undiv div-exp
19×associate-*r* associate-/r*
13×associate-*l*
12×prod-exp cbrt-unprod
9×distribute-lft-out
7×div-inv associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down associate-/r/ *-commutative
Counts
4 → 179
Calls
4 calls:
85.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
46.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
511.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
848.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
176.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
101.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify118.0ms

Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08383659
148932981
250012981
done50012981

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.3b

regimes152.0ms

Accuracy

42.9% (2.1b remaining)

Error of 38.6b against oracle of 36.5b and baseline of 40.2b

bsearch45.0ms

Steps
ItersRangePoint
6
4.695572007053586e+153
3.850595089123329e+154
1.1430115503814212e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02860
12860
done2860

end0.0ms

sample678.0ms

Algorithm
intervals
Results
339.0ms8000×body80valid
104.0ms8000×pre80true