Details

Time bar (total: 19.7s)

sample27.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms256×pre80true

simplify881.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01435
13335
211831
352231
4268931
done500031

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

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)))
2.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite95.0ms

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:
14.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
41.0ms
(/ (/ (/ (+ 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)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series394.0ms

Counts
3 → 9
Calls
3 calls:
146.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
163.0ms
(/ (/ (/ (+ 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)))
84.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.8s

Counts
466 → 466
Iterations

Useful iterations: 2 (429.0ms)

IterNodesCost
050323454
1121322764
2496221815
done500021815

prune922.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
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
(/ (log1p (expm1 (/ (/ (+ 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)))
2.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
123×times-frac
72×add-sqr-sqrt add-cube-cbrt
28×distribute-lft-out
23×associate-/l*
13×add-exp-log add-cbrt-cube
11×associate-/r*
7×div-inv
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×flip3-+ associate-/r/ flip-+
1×log1p-udef log1p-expm1
Counts
4 → 169
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
12.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
17.0ms
(/ (log1p (expm1 (/ (/ (+ 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)))

series650.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
144.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
202.0ms
(/ (log1p (expm1 (/ (/ (+ 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)))

simplify789.0ms

Counts
181 → 181
Iterations

Useful iterations: 2 (194.0ms)

IterNodesCost
02596491
15986239
222445768
done50015768

prune555.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

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)))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
10.8b
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
7310×times-frac
3890×*-un-lft-identity
2930×add-sqr-sqrt
2924×add-cube-cbrt
1932×sqrt-prod
483×distribute-lft-out
187×div-inv
83×associate-/r*
36×add-exp-log
32×associate-/l*
27×associate-/r/ add-cbrt-cube
25×div-exp
16×cbrt-undiv
6×pow1 sqrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ 1-exp flip-+ associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
Counts
4 → 2219
Calls
4 calls:
12.0ms
(/ (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))))
71.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
47.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
52.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
156.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

simplify887.0ms

Counts
2231 → 2231
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
02280160871
done5000160859

prune8.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize23.0ms

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
(/ 1 (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
140×*-un-lft-identity
110×add-sqr-sqrt
104×add-cube-cbrt
72×sqrt-prod
28×associate-/r*
18×distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
10×associate-/l*
8×div-exp
7×pow1
6×sqrt-div div-inv
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num hypot-def associate-/l/
1×pow-flip associate-/r/ inv-pow
Counts
4 → 211
Calls
4 calls:
8.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
11.0ms
(/ 1 (/ (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))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
255.0ms
(/ 1 (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
54.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
48.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.3s

Counts
223 → 223
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02746164
16455570
222385073
done50005065

prune629.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes82.0ms

Accuracy

55.1% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch33.0ms

Steps
ItersRangePoint
5
1.2761513080479214e+167
3.467445464211409e+167
3.2116744201778903e+167

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02249
12549
done2549

end0.0ms

sample540.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
106.0ms8000×pre80true