Details

Time bar (total: 18.6s)

sample27.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms256×pre80true

simplify961.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01435
13335
211831
351531
4264831
done500031

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
2.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
765×*-un-lft-identity
360×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 457
Calls
3 calls:
11.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
43.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series388.0ms

Counts
3 → 9
Calls
3 calls:
142.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
161.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
85.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.7s

Counts
466 → 466
Iterations

Useful iterations: 2 (750.0ms)

IterNodesCost
050323454
1120422764
2411921815
done500121815

prune909.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite656.0ms

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:
62.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
168.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
250.0ms
(/ (/ (/ (+ (+ (+ 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))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
131.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms
(/ (/ (/ (+ (+ (+ 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))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify582.0ms

Counts
488 → 488
Iterations

Useful iterations: done (554.0ms)

IterNodesCost
061126134
1151224802
done500024645

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
0.1b
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
2.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log *-un-lft-identity
55×add-sqr-sqrt
54×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
16×associate-*l* prod-exp
15×cbrt-undiv
13×associate-*r* distribute-lft-out
11×associate-/r*
8×cbrt-unprod associate-/l*
7×pow1
6×associate-/l/ unswap-sqr
5×rec-exp 1-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times flip3-+ associate-*r/ associate-*l/ associate-/r/ un-div-inv flip-+
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 173
Calls
4 calls:
2.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
24.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
24.0ms
(/ (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
143.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
162.0ms
(/ (* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
83.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify926.0ms

Counts
185 → 185
Iterations

Useful iterations: 2 (325.0ms)

IterNodesCost
02395126
16844814
224894059
done50014059

prune436.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.9b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
10.8b
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
7310×times-frac
3890×*-un-lft-identity
2930×add-sqr-sqrt
2924×add-cube-cbrt
1932×sqrt-prod
483×distribute-lft-out
187×div-inv
83×associate-/r*
36×add-exp-log
32×associate-/l*
27×associate-/r/ add-cbrt-cube
25×div-exp
16×cbrt-undiv
6×pow1 sqrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ 1-exp flip-+ associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
Counts
4 → 2219
Calls
4 calls:
8.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
4.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
70.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
54.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
48.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
151.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))))

simplify881.0ms

Counts
2231 → 2231
Iterations

Useful iterations: done (685.0ms)

IterNodesCost
02280160871
done5000160859

prune7.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.7b

regimes116.0ms

Accuracy

91.5% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 3.6b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02183
12983
done2983

end0.0ms

sample553.0ms

Algorithm
intervals
Results
313.0ms8000×body80valid
97.0ms8000×pre80true