Details

Time bar (total: 19.0s)

sample54.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
6.0ms256×pre80true

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize36.0ms

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:
37.0ms
(/ (/ (+ 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))
19.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series545.0ms

Counts
3 → 9
Calls
3 calls:
169.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
221.0ms
(/ (/ (/ (+ 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))
154.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.2s

Counts
413 → 413
Iterations

Useful iterations: done (2.1s)

IterNodesCost
050020409
1114119797
2320518977
done500218368

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
16×associate-*l* prod-exp
15×cbrt-undiv
13×associate-*r*
10×associate-/r*
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×associate-/l/ unswap-sqr
5×rec-exp 1-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times flip3-+ associate-*r/ associate-*l/ associate-/r/ un-div-inv flip-+
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 171
Calls
4 calls:
5.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
55.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
39.0ms
(/ (* (/ (+ 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))
38.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
199.0ms
(* (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
225.0ms
(/ (* (/ (+ 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))
109.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.9s

Counts
183 → 183
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02365066
16214640
220914002
done50024001

prune666.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

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)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
0.5b
(/ (* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
2.0b
(* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log
34×add-cbrt-cube
31×add-sqr-sqrt
27×*-un-lft-identity
22×add-cube-cbrt
21×times-frac
18×div-exp prod-exp
17×associate-*r*
10×cbrt-undiv cbrt-unprod
9×pow1
7×associate-*l*
6×flip3-+ associate-*r/ flip-+ associate-/l/
4×expm1-log1p-u frac-times rec-exp 1-exp associate-*l/ associate-/r* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×div-inv
2×frac-2neg pow-prod-down clear-num associate-/r/ un-div-inv *-commutative distribute-lft-out
1×distribute-rgt-in pow-flip distribute-lft-in inv-pow
Counts
4 → 140
Calls
4 calls:
9.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
35.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
42.0ms
(/ (* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
57.0ms
(* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
59.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
265.0ms
(/ (* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta)))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
133.0ms
(* (+ 1.0 (fma alpha beta (+ alpha beta))) (/ 1 (fma 1.0 2.0 (+ alpha beta))))

simplify1.7s

Counts
152 → 152
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02173818
15903436
226812868
done50002862

prune525.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
0.4b
(expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
0.5b
(/ (expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
1.9b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
19×add-sqr-sqrt
17×add-cube-cbrt
15×times-frac
13×add-exp-log add-cbrt-cube
7×associate-/l*
6×pow1
5×distribute-lft-out
4×expm1-log1p-u associate-*r/ associate-*r* associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ div-exp associate-*l* flip-+
2×frac-2neg prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l/ expm1-udef
1×distribute-rgt-in expm1-log1p distribute-lft-in div-sub pow-prod-down *-commutative unswap-sqr
Counts
4 → 97
Calls
4 calls:
22.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
0.0ms
(expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
13.0ms
(/ (expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
39.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series1.3s

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta))))
348.0ms
(expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
808.0ms
(/ (expm1 (log1p (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 1.0 (fma 1.0 2.0 (+ alpha beta)))))
135.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.4s

Counts
109 → 109
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01722871
14032706
215132385
done50022373

prune466.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.4b

regimes82.0ms

Accuracy

60.8% (0.9b remaining)

Error of 2.1b against oracle of 1.2b and baseline of 3.6b

bsearch106.0ms

Steps
ItersRangePoint
10
3.787217848124224e+152
3.104754081890425e+165
1.3803104342099798e+163

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02460
13060
done3060

end0.0ms

sample1.3s

Algorithm
intervals
Results
794.0ms8000×body80valid
192.0ms8000×pre80true