Details

Time bar (total: 23.2s)

sample46.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify618.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01435
13335
211931
358931
done500031

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize48.0ms

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))
1.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

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:
447.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
659.0ms
(/ (/ (/ (+ (+ (+ 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))
354.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series548.0ms

Counts
3 → 9
Calls
3 calls:
195.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
209.0ms
(/ (/ (/ (+ (+ (+ 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))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify697.0ms

Counts
465 → 465
Iterations

Useful iterations: done (659.0ms)

IterNodesCost
058525879
1148125086
done500021722

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta)))
1.7b
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
15.1b
(* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite720.0ms

Algorithm
rewrite-expression-head
Rules
934×times-frac
557×*-un-lft-identity
429×add-sqr-sqrt
415×add-cube-cbrt
166×associate-*l*
71×distribute-lft-out
59×associate-/l*
49×add-cbrt-cube add-exp-log
32×div-inv
24×cbrt-undiv div-exp
16×associate-/r/
11×flip3-- flip--
10×associate-/r*
8×prod-diff prod-exp cbrt-unprod associate-/l/
7×distribute-rgt-in distribute-lft-in
6×pow1
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×sub-neg flip3-+ associate-*l/ associate--l+ flip-+
1×pow-prod-down *-commutative
Counts
4 → 522
Calls
4 calls:
274.0ms
(/ (* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
115.0ms
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta)))
14.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
278.0ms
(* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series884.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
259.0ms
(/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta)))
135.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
230.0ms
(* (/ (/ (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 2.0 1.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify978.0ms

Counts
534 → 534
Iterations

Useful iterations: done (930.0ms)

IterNodesCost
075025796
1208925170
done500124017

prune3.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (+ (fma beta alpha (+ alpha beta)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.7b
(sqrt (+ (fma beta alpha (+ alpha beta)) 1.0))
1.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite501.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
80×sqrt-prod
70×times-frac
60×add-sqr-sqrt
54×add-cube-cbrt
22×distribute-lft-out
13×associate-/r*
11×associate-/l*
10×sqrt-div
8×add-cbrt-cube add-exp-log
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
1×sqrt-undiv
Counts
4 → 169
Calls
4 calls:
22.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (+ (fma beta alpha (+ alpha beta)) 1.0)))
269.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
12.0ms
(sqrt (+ (fma beta alpha (+ alpha beta)) 1.0))
193.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series682.0ms

Counts
4 → 12
Calls
4 calls:
369.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (+ (fma beta alpha (+ alpha beta)) 1.0)))
166.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms
(sqrt (+ (fma beta alpha (+ alpha beta)) 1.0))
77.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.4s

Counts
181 → 181
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02844932
16294280
225894132
done50024123

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)
0.1b
(/ (/ (cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.7b
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
2.4b
(cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
1551×times-frac
1129×*-un-lft-identity
657×add-sqr-sqrt add-cube-cbrt
608×cbrt-prod
272×unpow-prod-down cube-prod
236×distribute-lft-out
133×associate-/l*
41×div-inv
17×cube-mult unpow3 sqr-pow
14×add-exp-log
13×add-cbrt-cube
12×associate-/r/
7×associate-/r* flip3-+ flip-+
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/l/
2×cube-div clear-num frac-2neg pow-exp rem-cube-cbrt
1×pow-to-exp cbrt-div pow-pow pow1/3 rem-cbrt-cube
Counts
4 → 807
Calls
4 calls:
18.0ms
(pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)
336.0ms
(/ (/ (cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
30.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
20.0ms
(cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3))

series782.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)
251.0ms
(/ (/ (cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
118.0ms
(/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta)))
118.0ms
(cbrt (pow (/ (+ (fma beta alpha (+ alpha beta)) 1.0) (fma 2.0 1.0 (+ alpha beta))) 3))

simplify1.2s

Counts
819 → 819
Iterations

Useful iterations: done (1.1s)

IterNodesCost
079549136
1211942094
done500040412

prune2.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

regimes171.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01748
12348
done2348

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8000×body80valid
255.0ms8000×pre80true