Details

Time bar (total: 25.8s)

sample43.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
5.0ms256×pre80true

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
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))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
2.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg flip3-+ clear-num flip-+
2×associate-/r/
1×+-commutative associate-+l+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
9.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
25.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
49.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
18.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
193.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
212.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
110.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.3s

Counts
434 → 434
Iterations

Useful iterations: done (2.2s)

IterNodesCost
051620618
1117520002
2327719166
done500018557

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
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))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
2.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
600×times-frac
383×*-un-lft-identity
279×add-sqr-sqrt add-cube-cbrt
72×associate-/l*
52×distribute-lft-out
23×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp
9×associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg flip3-+ clear-num flip-+
2×associate-/r/
1×+-commutative associate-+r+ fma-def
Counts
4 → 368
Calls
4 calls:
81.0ms
(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
27.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
171.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
26.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (* 1.0 2.0) (+ (+ alpha beta) 1.0))
157.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
180.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (* 1.0 2.0) (+ (+ alpha beta) 1.0)))
119.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.9s

Counts
380 → 380
Iterations

Useful iterations: done (1.9s)

IterNodesCost
052918010
1123017218
2384316397
done500015894

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
0.4b
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
2.4b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.4b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
612×times-frac
516×sqrt-prod
421×*-un-lft-identity
325×add-sqr-sqrt
319×add-cube-cbrt
53×associate-/l*
51×distribute-lft-out
12×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1 sqrt-div
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×sqrt-undiv flip3-+ flip-+ associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
Counts
4 → 456
Calls
4 calls:
44.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
30.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
8.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series584.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
154.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
88.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
81.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify3.5s

Counts
468 → 468
Iterations

Useful iterations: done (3.5s)

IterNodesCost
042120141
193017784
2176816794
3448616207
done500016201

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize22.0ms

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)))) (fma 1.0 2.0 (+ (+ alpha beta) 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)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
2.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
2.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite579.0ms

Algorithm
rewrite-expression-head
Rules
1069×times-frac
630×*-un-lft-identity
553×add-sqr-sqrt
470×add-cube-cbrt
443×sqrt-prod
169×associate-*r*
80×distribute-lft-out
63×associate-/l*
55×associate-*l*
36×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
9×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg sqrt-div clear-num
2×flip3-+ prod-exp cbrt-unprod flip-+
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 570
Calls
4 calls:
365.0ms
(* (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)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
51.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
45.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
34.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series685.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(* (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)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0))))
220.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ (+ alpha beta) 1.0)))
132.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
116.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.8s

Counts
582 → 582
Iterations

Useful iterations: done (2.8s)

IterNodesCost
077332756
1146031246
2395129412
done500028524

prune3.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes94.0ms

Accuracy

0% (2.8b remaining)

Error of 4.0b against oracle of 1.2b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01651
11951
done1951

end0.0ms

sample1.2s

Algorithm
intervals
Results
655.0ms8000×body80valid
235.0ms8000×pre80true