Details

Time bar (total: 39.2s)

sample46.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
6.0ms256×pre80true

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize14.0ms

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))
1.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite167.0ms

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:
25.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
70.0ms
(/ (/ (/ (+ 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))
27.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series612.0ms

Counts
3 → 9
Calls
3 calls:
235.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
265.0ms
(/ (/ (/ (+ 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))
113.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.2s

Counts
413 → 413
Iterations

Useful iterations: done (2.2s)

IterNodesCost
050020409
1114119797
2320518977
done500218368

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
0.0b
(/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
0.1b
(/ (/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
1.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
16525×times-frac
9078×*-un-lft-identity
6234×add-sqr-sqrt add-cube-cbrt
1422×distribute-lft-out
714×associate-/l*
648×div-inv
154×add-exp-log
134×div-exp
88×associate-/r/
76×associate-/r*
61×add-cbrt-cube
41×cbrt-undiv
30×1-exp
12×rec-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
2×flip3-+ flip-+
Counts
4 → 4433
Calls
4 calls:
31.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
65.0ms
(/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
361.0ms
(/ (/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
18.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series758.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
227.0ms
(/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
245.0ms
(/ (/ (/ 1 1) (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
99.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify6.4s

Counts
4445 → 4445
Iterations

Useful iterations: done (6.0s)

IterNodesCost
04634286834
done5000264013

prune12.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 1) (* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
0.1b
(/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ 1 (+ 1.0 (fma alpha beta (+ alpha beta))))
15.8b
(* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
819×add-exp-log
659×div-exp
378×times-frac
222×*-un-lft-identity
199×add-sqr-sqrt
179×1-exp
160×prod-exp
159×add-cube-cbrt
116×rec-exp
113×add-cbrt-cube
67×cbrt-undiv
44×associate-*r*
28×distribute-lft-out
26×associate-/l*
23×associate-/r/
22×div-inv
21×associate-/r*
18×associate-*l* cbrt-unprod
12×unswap-sqr
10×pow1
6×frac-times associate-*r/ associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
2×pow-flip inv-pow pow-div
1×pow-prod-down *-commutative associate-/l/
Counts
4 → 511
Calls
4 calls:
63.0ms
(/ (/ (/ 1 1) (* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
10.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
12.0ms
(/ 1 (+ 1.0 (fma alpha beta (+ alpha beta))))
85.0ms
(* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(/ (/ (/ 1 1) (* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
35.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
77.0ms
(/ 1 (+ 1.0 (fma alpha beta (+ alpha beta))))
220.0ms
(* (/ 1 (+ 1.0 (fma alpha beta (+ alpha beta)))) (/ (fma 1.0 2.0 (+ alpha beta)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))

simplify2.7s

Counts
523 → 523
Iterations

Useful iterations: done (2.6s)

IterNodesCost
087320941
1172116280
2375014815
done500014669

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
0.1b
(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
15.8b
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log
34×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
28×times-frac
25×add-cube-cbrt
18×div-exp prod-exp
16×associate-*l*
14×associate-*r*
10×cbrt-undiv cbrt-unprod
9×pow1
7×associate-*r/ associate-/l*
4×expm1-log1p-u rec-exp flip3-+ 1-exp associate-/r* associate-/r/ flip-+ log1p-expm1-u div-inv distribute-lft-out add-log-exp unswap-sqr
2×frac-2neg pow-prod-down clear-num *-commutative associate-/l/
1×distribute-rgt-in frac-times pow-flip distribute-lft-in associate-*l/ inv-pow
Counts
4 → 145
Calls
4 calls:
11.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
25.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
103.0ms
(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
51.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
64.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
236.0ms
(* (/ 1 (fma 1.0 2.0 (+ alpha beta))) (/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
233.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))

simplify1.8s

Counts
157 → 157
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02154430
15774124
223723504
done50003499

prune543.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes68.0ms

Accuracy

70.5% (1.2b remaining)

Error of 1.5b against oracle of 0.3b and baseline of 4.4b

bsearch96.0ms

Steps
ItersRangePoint
10
3.787217848124224e+152
3.104754081890425e+165
2.4580673707165206e+153

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02765
13561
done3561

end0.0ms

sample1.8s

Algorithm
intervals
Results
760.0ms8000×body80valid
744.0ms8000×pre80true