Details

Time bar (total: 12.5s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify1.1s

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: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
766×*-un-lft-identity
361×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×flip3-+ associate-/r/ flip-+
1×fma-udef
Counts
4 → 467
Calls
4 calls:
0.0ms
(fma alpha beta (+ alpha beta))
12.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
44.0ms
(/ (/ (/ (+ 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)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(fma alpha beta (+ alpha beta))
147.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
163.0ms
(/ (/ (/ (+ 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)))
86.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.5s

Counts
479 → 479
Iterations

Useful iterations: 2 (774.0ms)

IterNodesCost
051323562
1122222869
2414921908
done500121908

prune969.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ alpha beta))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* 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)))
3.6b
(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
766×*-un-lft-identity
361×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg flip3-+ clear-num sum-log flip-+
2×associate-/r/
1×+-commutative associate-+r+ fma-def
Counts
4 → 473
Calls
4 calls:
10.0ms
(+ (* alpha beta) (+ alpha beta))
77.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
104.0ms
(/ (/ (/ (+ 1.0 (+ (* 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)))
71.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (* alpha beta) (+ alpha beta))
147.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
162.0ms
(/ (/ (/ (+ 1.0 (+ (* 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)))
86.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.6s

Counts
485 → 485
Iterations

Useful iterations: 2 (817.0ms)

IterNodesCost
052924361
1130522934
2457921973
done500021973

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma alpha beta (+ alpha beta))
0.0b
(/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
3.6b
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
68×times-frac
41×add-exp-log
35×add-sqr-sqrt add-cube-cbrt
29×add-cbrt-cube
28×distribute-lft-out
21×div-exp
13×cbrt-undiv
12×associate-/l*
11×associate-/r*
9×div-inv
8×prod-exp
4×pow1 expm1-log1p-u 1-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×flip3-+ associate-/r/ flip-+
1×associate-*r/ fma-udef
Counts
4 → 145
Calls
4 calls:
0.0ms
(fma alpha beta (+ alpha beta))
7.0ms
(/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
25.0ms
(/ (/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
11.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(fma alpha beta (+ alpha beta))
154.0ms
(/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
167.0ms
(/ (/ (* 1 (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
86.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify856.0ms

Counts
157 → 157
Iterations

Useful iterations: 2 (329.0ms)

IterNodesCost
02315455
16045134
224114567
done50014567

prune408.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite233.0ms

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:
82.0ms
(/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
67.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
50.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta))))
4.0ms
(sqrt (+ (fma alpha beta (+ alpha beta)) 1.0))

series439.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
117.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
47.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ alpha beta))))
59.0ms
(sqrt (+ (fma alpha beta (+ alpha beta)) 1.0))

simplify906.0ms

Counts
468 → 468
Iterations

Useful iterations: done (879.0ms)

IterNodesCost
045020865
1101517789
2240916796
done500016786

prune890.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

regimes67.0ms

Accuracy

56.4% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch58.0ms

Steps
ItersRangePoint
8
4.8266542845792594e+173
1.0069133071674746e+178
8.48564295701033e+177

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01946
12446
done2446

end0.0ms

sample540.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
96.0ms8000×pre80true