Details

Time bar (total: 50.4s)

sample60.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
17.0ms256×pre80true

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize29.0ms

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)))

rewrite216.0ms

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:
31.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
98.0ms
(/ (/ (/ (+ 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))
30.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series547.0ms

Counts
3 → 9
Calls
3 calls:
202.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
225.0ms
(/ (/ (/ (+ 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))
120.0ms
(/ (+ 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

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

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 (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
0.1b
(/ (/ 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)))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
3314×times-frac
2034×*-un-lft-identity
1330×add-sqr-sqrt add-cube-cbrt
352×distribute-lft-out
174×associate-/l*
89×div-inv
76×associate-/r*
64×add-exp-log
44×div-exp
34×add-cbrt-cube
28×associate-/r/
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-/l/
2×flip3-+ flip-+
1×pow-flip inv-pow
Counts
4 → 1214
Calls
4 calls:
22.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
35.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
162.0ms
(/ (/ 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))
19.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series887.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))
227.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
291.0ms
(/ (/ 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))
135.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify3.5s

Counts
1226 → 1226
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0140568287
1331563310
done500060980

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
18263×times-frac
9830×*-un-lft-identity
6810×add-sqr-sqrt add-cube-cbrt
1510×distribute-lft-out
746×associate-/l*
650×div-inv
552×associate-/r/
263×flip3-+ flip-+
260×associate-/r*
213×add-exp-log
177×div-exp
61×add-cbrt-cube
41×cbrt-undiv
32×rec-exp 1-exp
5×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×pow-flip inv-pow
Counts
4 → 4995
Calls
4 calls:
98.0ms
(/ 1 (/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))
429.0ms
(/ (/ 1 (/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
45.0ms
(/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
13.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0))

series839.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(/ 1 (/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta)))))
268.0ms
(/ (/ 1 (/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
207.0ms
(/ (/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0)) (/ 1 (fma 1.0 2.0 (+ alpha beta))))
128.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ (fma alpha beta (+ alpha beta)) 1.0))

simplify3.1s

Counts
5007 → 5007
Iterations

Useful iterations: 0 (871.0ms)

IterNodesCost
05186318996
done5186318996

prune25.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize15.0ms

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)))

rewrite156.0ms

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:
6.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
24.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
81.0ms
(* (/ 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))))
39.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (fma 1.0 2.0 (+ alpha beta)))
49.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
275.0ms
(* (/ 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))))
246.0ms
(/ (+ (fma alpha beta (+ alpha beta)) 1.0) (* (fma 1.0 2.0 (+ alpha beta)) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))

simplify1.6s

Counts
157 → 157
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02154430
15774124
223723504
done50003499

prune536.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes96.0ms

bsearch3.0ms