Details

Time bar (total: 15.0s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01435
13335
211831
351531
4264831
done500131

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
765×*-un-lft-identity
360×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 457
Calls
3 calls:
12.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
40.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
11.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series384.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
159.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
83.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.2s

Counts
466 → 466
Iterations

Useful iterations: 2 (688.0ms)

IterNodesCost
050323454
1120422764
2381421815
done500021815

prune888.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (* 1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
113×times-frac
105×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
33×add-exp-log
24×add-cbrt-cube
22×distribute-lft-out
21×associate-/l*
17×div-exp
11×cbrt-undiv associate-/r*
7×div-inv
6×prod-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg 1-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
1×associate-*r/
Counts
3 → 156
Calls
3 calls:
12.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
29.0ms
(/ (* 1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series390.0ms

Counts
3 → 9
Calls
3 calls:
147.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
161.0ms
(/ (* 1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
81.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify919.0ms

Counts
165 → 165
Iterations

Useful iterations: 2 (324.0ms)

IterNodesCost
02565776
16645586
221364963
done50004963

prune412.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.2b
(* (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
3.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×*-un-lft-identity
46×times-frac
45×sqrt-prod
38×add-cube-cbrt
25×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div distribute-lft-out
8×pow1
7×associate-*l* associate-/l*
6×unswap-sqr
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod hypot-def div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 143
Calls
4 calls:
8.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
27.0ms
(* (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
4.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
83.0ms
(* (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
53.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
54.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify2.8s

Counts
155 → 155
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01883974
14373459
212643168
348803092
done50003092

prune499.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
1625×times-frac
1425×*-un-lft-identity
721×add-sqr-sqrt
651×sqrt-prod
638×add-cube-cbrt
449×distribute-lft-out
281×associate-*r*
63×associate-/l*
55×associate-*l*
52×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
11×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u flip3-+ div-exp associate-/r/ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 796
Calls
4 calls:
309.0ms
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
47.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
137.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
83.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
76.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.8s

Counts
808 → 808
Iterations

Useful iterations: 2 (981.0ms)

IterNodesCost
078445242
1165842882
2422440480
done500140480

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.4b

regimes92.0ms

Accuracy

42.7% (1.4b remaining)

Error of 2.5b against oracle of 1.1b and baseline of 3.5b

bsearch76.0ms

Steps
ItersRangePoint
10
2.101796536226482e+99
1.0007381237611808e+112
9.80954730625927e+111

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02766
13562
done3562

end0.0ms

sample538.0ms

Algorithm
intervals
Results
292.0ms8000×body80valid
100.0ms8000×pre80true