Details

Time bar (total: 25.4s)

sample61.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
6.0ms256×pre80true

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
33.0ms
(+ (+ alpha beta) (* beta alpha))
455.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
657.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
413.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (+ alpha beta) (* beta alpha))
186.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
210.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
104.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify997.0ms

Counts
487 → 487
Iterations

Useful iterations: done (953.0ms)

IterNodesCost
061226076
1148924596
done500021873

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (* (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))))))
3.0b
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
3.0b
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
3.0b
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
25×cbrt-prod
15×distribute-lft-out
13×add-exp-log
11×add-sqr-sqrt add-cube-cbrt
9×add-cbrt-cube
8×cbrt-div times-frac associate-/l*
6×flip3-+ flip-+
5×associate-/r/
4×pow1 cbrt-undiv expm1-log1p-u sqrt-div div-exp log1p-expm1-u add-log-exp
3×pow1/3
2×frac-times associate-*l/ prod-exp cbrt-unprod associate-/l/
1×frac-2neg associate-*r/ clear-num associate-/r* div-inv
Counts
4 → 93
Calls
4 calls:
105.0ms
(/ (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (* (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))))))
13.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
13.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
23.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
422.0ms
(/ (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (* (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (/ (sqrt (fma 1.0 2.0 (+ alpha beta))) (cbrt (+ 1.0 (+ alpha (fma alpha beta beta)))))))
80.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
126.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))
80.0ms
(cbrt (+ 1.0 (+ alpha (fma alpha beta beta))))

simplify1.2s

Counts
105 → 105
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02053221
15343061
215862803
done50012727

prune715.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
0.8b
(* (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
3754×times-frac
2592×*-un-lft-identity
1724×add-sqr-sqrt
1526×sqrt-prod
1502×add-cube-cbrt
622×associate-*r*
617×distribute-lft-out
88×associate-/l*
63×div-inv
62×associate-*l*
45×add-exp-log add-cbrt-cube unswap-sqr
22×cbrt-undiv div-exp
10×sqrt-div
8×pow1 prod-exp cbrt-unprod
7×associate-/r*
6×associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1531
Calls
4 calls:
128.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
1.2s
(* (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
39.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
74.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

series992.0ms

Counts
4 → 12
Calls
4 calls:
582.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
265.0ms
(* (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ alpha (fma alpha beta beta)))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
79.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
66.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

simplify2.6s

Counts
1543 → 1543
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0122194405
1337787447
done500084020

prune4.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

localize68.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
2.6b
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
20×add-sqr-sqrt sqrt-prod
12×distribute-lft-out
8×pow1 add-cube-cbrt sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ hypot-def log1p-expm1-u add-log-exp
Counts
4 → 80
Calls
4 calls:
42.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
32.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
35.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
57.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
74.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
83.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))
84.0ms
(sqrt (+ 1.0 (+ alpha (fma alpha beta beta))))

simplify1.1s

Counts
92 → 92
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0561268
11361108
23781068
313221052
done50001044

prune595.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.9b

regimes141.0ms

Accuracy

88.4% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 3.6b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
026102
136102
done36102

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s8000×body80valid
165.0ms8000×pre80true