Details

Time bar (total: 1.4m)

sample62.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
7.0ms256×pre80true

simplify585.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01435
13335
211931
359331
done500131

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma alpha beta (+ alpha beta)))
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))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg flip3-+ clear-num flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
6.0ms
(+ 1.0 (fma alpha beta (+ alpha beta)))
40.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
77.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
29.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ 1.0 (fma alpha beta (+ alpha beta)))
235.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
229.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
121.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify753.0ms

Counts
434 → 434
Iterations

Useful iterations: done (711.0ms)

IterNodesCost
051420622
1132719999
done500119195

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize55.0ms

Local error

Found 4 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
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
0.3b
(/ (/ (/ 1 1) 1) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
3.6b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
47955×times-frac
25330×*-un-lft-identity
17358×add-sqr-sqrt add-cube-cbrt
3986×distribute-lft-out
1632×div-inv
271×associate-/r*
250×add-exp-log
248×div-exp
74×add-cbrt-cube
68×1-exp
67×associate-/l*
52×cbrt-undiv
46×associate-/r/
16×rec-exp
6×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ flip-+
Counts
4 → 9905
Calls
4 calls:
42.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
79.0ms
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
451.0ms
(/ (/ (/ 1 1) 1) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
26.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series864.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
323.0ms
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
265.0ms
(/ (/ (/ 1 1) 1) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
95.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify6.3s

Counts
9917 → 9917
Iterations

Useful iterations: 0 (1.2s)

IterNodesCost
010276787959
done10276787959

prune58.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
0.5b
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
3.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
612×times-frac
516×sqrt-prod
421×*-un-lft-identity
325×add-sqr-sqrt
319×add-cube-cbrt
53×associate-/l*
51×distribute-lft-out
12×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1 sqrt-div
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×sqrt-undiv flip3-+ flip-+ associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
Counts
4 → 456
Calls
4 calls:
63.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
33.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
9.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
148.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
74.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
55.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify740.0ms

Counts
468 → 468
Iterations

Useful iterations: done (696.0ms)

IterNodesCost
042120141
1103017784
done500116964

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite389.0ms

Algorithm
rewrite-expression-head
Rules
886×times-frac
802×*-un-lft-identity
368×add-sqr-sqrt add-cube-cbrt
248×distribute-lft-out
85×associate-/l*
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg flip3-+ clear-num sum-log flip-+
2×associate-/r/
1×+-commutative associate-+r+
Counts
4 → 485
Calls
4 calls:
19.0ms
(+ alpha (+ 1.0 beta))
102.0ms
(/ (/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
88.0ms
(/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta)))
124.0ms
(/ (/ (/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))

series405.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ alpha (+ 1.0 beta))
153.0ms
(/ (/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
64.0ms
(/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta)))
175.0ms
(/ (/ (/ (+ alpha (+ 1.0 beta)) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))

simplify748.0ms

Counts
497 → 497
Iterations

Useful iterations: done (723.0ms)

IterNodesCost
051821502
1134320787
done500119933

prune2.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes178.0ms

Accuracy

56.8% (1.3b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 4.2b

bsearch107.0ms

Steps
ItersRangePoint
9
7.341643047563169e+165
1.1087289815306716e+171
1.6300639746541218e+170

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02469
13165
done3165

end0.0ms

sample1.3s

Algorithm
intervals
Results
788.0ms8000×body80valid
179.0ms8000×pre80true