Details

Time bar (total: 9.5s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify879.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01435
13335
211831
352231
4268931
done500031

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

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)))
5.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite103.0ms

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:
12.0ms
(/ (/ (+ 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)))

series402.0ms

Counts
3 → 9
Calls
3 calls:
153.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
164.0ms
(/ (/ (/ (+ 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)))

simplify1.6s

Counts
466 → 466
Iterations

Useful iterations: 2 (422.0ms)

IterNodesCost
050323454
1121322764
2496221815
done500021815

prune956.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ 1.0 (fma alpha beta (+ 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))))
5.0b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
5.0b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
112×sqrt-prod
98×*-un-lft-identity
84×times-frac
72×add-sqr-sqrt
66×add-cube-cbrt
16×distribute-lft-out
14×associate-/l*
12×associate-/r*
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
4 → 182
Calls
4 calls:
9.0ms
(/ (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)))) (sqrt (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))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
114.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
55.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
51.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify908.0ms

Counts
194 → 194
Iterations

Useful iterations: 3 (251.0ms)

IterNodesCost
01525112
12904636
27314480
322084466
done50014466

prune790.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
2.4b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
5.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
52×times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
20×associate-/l*
19×add-exp-log add-cbrt-cube
13×distribute-lft-out
7×cbrt-undiv div-exp
5×pow1 associate-*l*
4×associate-*l/ associate-/r* div-inv
3×expm1-log1p-u flip3-+ associate-*r* prod-exp cbrt-unprod flip-+ log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num associate-/r/ fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 117
Calls
3 calls:
41.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
23.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
8.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series288.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
165.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
83.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify686.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (159.0ms)

IterNodesCost
01983814
15133768
222363324
done50013324

prune348.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (fma 1.0 2.0 (+ alpha beta)))
0.7b
(cbrt (fma 1.0 2.0 (+ alpha beta)))
5.0b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
5.0b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity
8×add-cube-cbrt sqrt-prod
6×pow1 cbrt-prod
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+ hypot-def distribute-lft-out
Counts
4 → 64
Calls
4 calls:
0.0ms
(cbrt (fma 1.0 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma 1.0 2.0 (+ alpha beta)))
7.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(cbrt (fma 1.0 2.0 (+ alpha beta)))
104.0ms
(cbrt (fma 1.0 2.0 (+ alpha beta)))
54.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
49.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify614.0ms

Counts
76 → 76
Iterations

Useful iterations: 3 (202.0ms)

IterNodesCost
01121074
1245978
2601928
31905874
done5000874

prune383.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.8b

regimes78.0ms

Accuracy

55.5% (1.1b remaining)

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

bsearch68.0ms

Steps
ItersRangePoint
9
1.68690722297182e+158
2.212909629018009e+163
6.85580170450604e+160

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02578
12978
done2978

end0.0ms

sample556.0ms

Algorithm
intervals
Results
310.0ms8000×body80valid
99.0ms8000×pre80true