Details

Time bar (total: 51.4s)

sample69.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
7.0ms256×pre80true

simplify608.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

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-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv associate-/r* div-exp
6×sum-log
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
138.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
441.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
603.0ms
(/ (/ (/ (+ (+ (+ 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))
458.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
208.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
201.0ms
(/ (/ (/ (+ (+ (+ 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))
131.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify793.0ms

Counts
488 → 488
Iterations
IterNodes
done5001
11537
0610

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.5b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.9b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
11532×times-frac
7080×*-un-lft-identity
4556×add-sqr-sqrt add-cube-cbrt
3150×sqrt-prod
1262×distribute-lft-out
734×associate-/l*
149×div-inv
54×associate-/r/
40×sqrt-div
34×add-cbrt-cube add-exp-log
28×flip3-+ flip-+
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
Counts
4 → 3658
Calls
4 calls:
194.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
602.0ms
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
55.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
24.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series1.1s

Counts
4 → 12
Calls
4 calls:
417.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
324.0ms
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
171.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
181.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify2.4s

Counts
3670 → 3670
Iterations
IterNodes
done5001
02680

prune19.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize117.0ms

Local error

Found 4 expressions with local error:

1.6b
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (* (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha)))) (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha))))))
5.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
5.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
5.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
16×add-exp-log
13×*-un-lft-identity
12×cbrt-prod
9×flip3-+ flip-+
8×add-cbrt-cube associate-/l/
7×add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u frac-times pow1 cbrt-undiv div-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow1/3 distribute-lft-out
2×associate-*l/ associate-*r/
1×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
43.0ms
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (* (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha)))) (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha))))))
7.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series507.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (* (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha)))) (cbrt (sqrt (fma 2.0 1.0 (+ beta alpha))))))
85.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
83.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
86.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify900.0ms

Counts
91 → 91
Iterations
IterNodes
done5001
21220
1424
0157

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0))))
0.0b
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0)))
1.9b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
4788×times-frac
2658×*-un-lft-identity
1682×add-sqr-sqrt add-cube-cbrt
488×distribute-lft-out
365×associate-/r/
361×difference-of-squares
183×div-inv
104×associate-/l*
100×flip3-- flip--
84×flip3-+ flip-+
34×add-cbrt-cube add-exp-log
28×associate-/r*
20×cbrt-undiv div-exp
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
Counts
4 → 1713
Calls
4 calls:
553.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0))))
52.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0)))
401.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
308.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
360.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0))))
85.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (- (+ beta alpha) (* 2.0 1.0)))
248.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
108.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.2s

Counts
1725 → 1725
Iterations
IterNodes
done5000
02273

prune12.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes234.0ms

Accuracy

51.8% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.9b

bsearch148.0ms

Steps
ItersRangePoint
8
1.842274828350243e+215
1.0430713603340258e+218
1.9343124020549875e+215

simplify11.0ms

Iterations
IterNodes
done43
143
036

end0.0ms

sample1.4s

Algorithm
intervals
Results
840.0ms8000×body80valid
210.0ms8000×pre80true