Details

Time bar (total: 24.9s)

sample64.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
6.0ms256×pre80true

simplify491.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize24.0ms

Local error

Found 3 expressions with local error:

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))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
Counts
3 → 456
Calls
3 calls:
404.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
516.0ms
(/ (/ (/ (+ (+ (+ 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))
375.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series534.0ms

Counts
3 → 9
Calls
3 calls:
184.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
251.0ms
(/ (/ (/ (+ (+ (+ 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))
98.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify730.0ms

Counts
465 → 465
Iterations
IterNodes
done5000
11481
0585

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha (- beta (* 2.0 1.0))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
0.0b
(/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0))))
0.1b
(/ (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0)))) (fma 2.0 1.0 (+ beta alpha)))
2.2b
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

rewrite555.0ms

Algorithm
rewrite-expression-head
Rules
976×times-frac
961×*-un-lft-identity
397×add-sqr-sqrt add-cube-cbrt
318×distribute-lft-out
110×associate-/l*
29×div-inv
22×add-cbrt-cube add-exp-log
15×associate-/r*
12×associate-/r/
11×cbrt-undiv div-exp
8×flip3-+ flip-+
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-+r- div-sub
Counts
4 → 555
Calls
4 calls:
108.0ms
(/ (+ alpha (- beta (* 2.0 1.0))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
120.0ms
(/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0))))
173.0ms
(/ (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0)))) (fma 2.0 1.0 (+ beta alpha)))
76.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (+ alpha (- beta (* 2.0 1.0))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
167.0ms
(/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0))))
264.0ms
(/ (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (+ alpha (- beta (* 2.0 1.0)))) (fma 2.0 1.0 (+ beta alpha)))
134.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

simplify939.0ms

Counts
567 → 567
Iterations
IterNodes
done5000
11696
0592

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta))))
0.1b
(* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))
0.1b
(/ (/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ beta alpha)))
2.2b
(/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0))))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
158×*-un-lft-identity
154×add-exp-log
104×div-exp
96×add-sqr-sqrt
91×add-cube-cbrt
61×add-cbrt-cube
38×distribute-lft-out
35×associate-/l*
31×cbrt-undiv
30×1-exp prod-exp
26×associate-*l*
14×div-inv
12×rec-exp
10×cbrt-unprod
9×associate-/r* associate-/r/
6×pow1 associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg flip3-+ associate-*r* flip-+
2×fma-udef unswap-sqr
1×distribute-rgt-in associate-+r- distribute-lft-in div-sub pow-prod-down *-commutative
Counts
4 → 282
Calls
4 calls:
38.0ms
(/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta))))
102.0ms
(* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))
55.0ms
(/ (/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ beta alpha)))
84.0ms
(/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0))))

series810.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta))))
187.0ms
(* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))
279.0ms
(/ (/ (/ 1 1) (* (/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0)))) (fma 2.0 1.0 (+ alpha beta)))) (fma 2.0 1.0 (+ beta alpha)))
153.0ms
(/ (+ beta (- alpha (* 1.0 2.0))) (+ alpha (+ beta (fma alpha beta 1.0))))

simplify730.0ms

Counts
294 → 294
Iterations
IterNodes
done5001
11298
0436

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
0.1b
(* (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0))))
2.2b
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))
2.2b
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1955×*-un-lft-identity
1937×times-frac
813×add-sqr-sqrt
759×sqrt-prod
735×distribute-lft-out
730×add-cube-cbrt
326×associate-*r*
74×associate-/l*
64×associate-*l*
52×div-inv
20×unswap-sqr
15×add-cbrt-cube add-exp-log
11×associate-/r*
6×pow1
5×associate-/l/
4×expm1-log1p-u cbrt-undiv flip3-+ div-exp associate-/r/ flip-+ log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-div
2×prod-exp cbrt-unprod
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 912
Calls
4 calls:
139.0ms
(/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
647.0ms
(* (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0))))
90.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))
93.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0)))
249.0ms
(* (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (+ (+ beta alpha) (fma 1.0 2.0 1.0))))
116.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))
137.0ms
(/ (+ (+ beta alpha) (fma alpha beta 1.0)) (fma 2.0 1.0 (+ beta alpha)))

simplify1.2s

Counts
924 → 924
Iterations
IterNodes
done5001
11779
0783

prune5.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

71.8% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 4.2b

bsearch132.0ms

Steps
ItersRangePoint
9
1.1416104037604334e+156
8.001771365916775e+161
1.8040289506123877e+158

simplify15.0ms

Iterations
IterNodes
done51
251
150
038

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8000×body80valid
197.0ms8000×pre80true