Details

Time bar (total: 1.2m)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize23.0ms

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))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
2.7b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
547×*-un-lft-identity
319×add-sqr-sqrt add-cube-cbrt
114×distribute-lft-out
72×associate-/l*
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
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 → 404
Calls
3 calls:
33.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
66.0ms
(/ (/ (/ (+ 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))
25.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series581.0ms

Counts
3 → 9
Calls
3 calls:
192.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
253.0ms
(/ (/ (/ (+ 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))
135.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.9s

Counts
413 → 413
Iterations

Useful iterations: done (1.9s)

IterNodesCost
050020409
1114119797
2320518977
done500218368

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
2.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.6b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.3b
(/ (/ (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)))))

rewrite691.0ms

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:
39.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
15.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
14.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
136.0ms
(/ (/ (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)))))

series680.0ms

Counts
4 → 12
Calls
4 calls:
313.0ms
(/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
70.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
94.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
202.0ms
(/ (/ (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)))))

simplify1.6s

Counts
2231 → 2231
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02280160871
done5000148277

prune8.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
0.2b
(/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
0.5b
(/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta))))
2.7b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
41816×times-frac
23168×*-un-lft-identity
15488×add-sqr-sqrt add-cube-cbrt
8544×sqrt-prod
3840×distribute-lft-out
1186×div-inv
165×associate-/l*
138×associate-/r/
84×associate-/r*
79×add-exp-log
57×div-exp
49×add-cbrt-cube
32×cbrt-undiv
13×pow1
8×pow-flip
6×pow-div
5×rec-exp sqrt-pow1 pow1/2 1-exp
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
2×inv-pow
1×flip3-+ flip-+
Counts
4 → 9894
Calls
4 calls:
370.0ms
(/ (/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
30.0ms
(/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
25.0ms
(/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta))))
39.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(/ (/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
43.0ms
(/ (/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
129.0ms
(/ 1 (sqrt (fma 1.0 2.0 (+ alpha beta))))
138.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify5.8s

Counts
9906 → 9906
Iterations

Useful iterations: 0 (1.6s)

IterNodesCost
07047868445
done7047868445

prune38.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.9b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.9b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
7.2b
(/ (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt
10×cbrt-div
9×add-exp-log
7×times-frac associate-/l*
6×add-cbrt-cube
5×flip3-+ flip-+ distribute-lft-out
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3
2×cbrt-undiv div-exp associate-*l/ associate-/r/ associate-/l/
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 83
Calls
4 calls:
8.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
46.0ms
(/ (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))

series787.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
103.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
93.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
517.0ms
(/ (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (* (cbrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))

simplify1.1s

Counts
95 → 95
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01942414
14872302
213462144
done50002088

prune656.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.9b

regimes101.0ms

Accuracy

58.7% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.9b

bsearch88.0ms

Steps
ItersRangePoint
6
2.050539660644998e+192
8.989128788768659e+192
3.0975586046167533e+192

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01636
11936
done1936

end0.0ms

sample1.3s

Algorithm
intervals
Results
820.0ms8000×body80valid
218.0ms8000×pre80true