Details

Time bar (total: 10.5s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify81.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113
done500113

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

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))
5.5b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
116.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
321.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
469.0ms
(/ (/ (/ (+ (+ (+ 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))
272.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
148.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
162.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify122.0ms

Counts
488 → 488
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151312983
1500212137
done500212137

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.5b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
214×times-frac
166×*-un-lft-identity
133×add-sqr-sqrt
112×add-cube-cbrt
61×add-exp-log add-cbrt-cube
54×associate-*l*
29×cbrt-undiv div-exp
27×distribute-lft-out
21×associate-/l*
15×associate-*r*
12×prod-exp cbrt-unprod div-inv
10×associate-/r*
8×associate-/r/
6×pow1 associate-/l/ unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
2×frac-times flip3-- associate-*r/ associate-*l/ flip--
1×pow-prod-down *-commutative
Counts
4 → 262
Calls
4 calls:
509.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
280.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
310.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
405.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
124.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
172.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
85.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify74.0ms

Counts
274 → 274
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012545927
150015094
done50015094

prune784.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite634.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
177.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
200.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
124.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
125.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series428.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
108.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify71.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05272718
119402545
250012473
done50012473

prune549.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
16.3b
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))))

rewrite758.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
142×add-exp-log
103×add-sqr-sqrt
101×*-un-lft-identity
92×add-cbrt-cube
91×add-cube-cbrt
61×div-exp
60×associate-*r*
49×prod-exp
35×cbrt-undiv
31×cbrt-unprod
20×frac-times associate-*l/
14×associate-/l*
12×flip3-+ flip-+ associate-/l/
11×pow1 div-inv
8×associate-/r/
7×associate-*r/ associate-/r*
6×rec-exp 1-exp associate-*l*
5×distribute-lft-out
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×flip3-- frac-2neg clear-num *-commutative flip--
Counts
4 → 269
Calls
4 calls:
248.0ms
(* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
40.0ms
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
313.0ms
(/ (* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
141.0ms
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))))

series532.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms
(/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
173.0ms
(/ (* (* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
129.0ms
(* (+ beta (+ alpha (fma alpha beta 1.0))) (/ (/ 1 (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))))

simplify77.0ms

Counts
281 → 281
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013885492
150014707
done50014707

prune792.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

regimes78.0ms

Accuracy

34.5% (1.6b remaining)

Error of 2.8b against oracle of 1.2b and baseline of 3.7b

bsearch46.0ms

Steps
ItersRangePoint
6
2.425829213074854e+127
3.660299660418296e+128
3.553719024558119e+128

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04547
14547
done4547

end0.0ms

sample560.0ms

Algorithm
intervals
Results
285.0ms8000×body80valid
84.0ms8000×pre80true