Details

Time bar (total: 16.9s)

sample42.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify608.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
1.7b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite146.0ms

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-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 404
Calls
3 calls:
24.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
56.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
36.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series669.0ms

Counts
3 → 9
Calls
3 calls:
242.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
267.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
159.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.0s

Counts
413 → 413
Iterations
IterNodes
done5001
11291
0500

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (* (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
0.1b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
1.7b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
1.7b
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha)))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
712×times-frac
478×sqrt-prod
441×*-un-lft-identity
311×add-sqr-sqrt add-cube-cbrt
145×associate-/l*
65×distribute-lft-out
31×add-cbrt-cube add-exp-log
25×div-inv
14×cbrt-undiv div-exp
13×associate-/r*
6×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×flip3-+ flip-+
1×sqrt-undiv sqrt-div associate-*l/ associate-/r/
Counts
4 → 488
Calls
4 calls:
89.0ms
(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (* (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
32.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
15.0ms
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha)))

series1.2s

Counts
4 → 12
Calls
4 calls:
582.0ms
(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (* (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
300.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
123.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
147.0ms
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (fma 2.0 1.0 (+ beta alpha)))

simplify718.0ms

Counts
500 → 500
Iterations
IterNodes
done5001
11492
0592

prune3.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
1.4b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
1.7b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
20×associate-/l*
19×add-cbrt-cube add-exp-log
11×distribute-lft-out
7×cbrt-undiv div-exp
5×pow1
4×associate-/r* associate-*r* associate-*r/ div-inv
3×expm1-log1p-u flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg associate-/r/
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 116
Calls
3 calls:
17.0ms
(* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
32.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series449.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
256.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
117.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.2s

Counts
125 → 125
Iterations
IterNodes
done5000
22575
1497
0191

prune842.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)
1.4b
(/ (cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
1.7b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha))
2.4b
(cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
240×*-un-lft-identity
197×times-frac
150×cbrt-prod
92×add-sqr-sqrt add-cube-cbrt
88×unpow-prod-down cube-prod
74×distribute-lft-out
57×associate-/l*
20×associate-/r/
14×add-exp-log
12×add-cbrt-cube
11×flip3-+ flip-+
10×div-inv
5×pow1 associate-/r*
4×expm1-log1p-u cube-mult cbrt-undiv unpow3 div-exp log1p-expm1-u add-log-exp sqr-pow
3×cube-div pow-unpow associate-/l/
2×cbrt-div clear-num frac-2neg pow-exp associate-*r/ rem-cube-cbrt
1×pow-to-exp pow-pow pow1/3 prod-exp rem-cbrt-cube cbrt-unprod
Counts
4 → 296
Calls
4 calls:
32.0ms
(pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)
112.0ms
(/ (cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
27.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha))
35.0ms
(cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3))

series747.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)
243.0ms
(/ (cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3)) (* (fma 2.0 1.0 (+ beta alpha)) (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
106.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha))
103.0ms
(cbrt (pow (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (+ (fma 2.0 1.0 beta) alpha)) 3))

simplify555.0ms

Counts
308 → 308
Iterations
IterNodes
done5000
1890
0306

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes170.0ms

Accuracy

57% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch121.0ms

Steps
ItersRangePoint
8
3.6123365310673503e+163
1.6928952919389437e+168
2.94435674190199e+166

simplify5.0ms

Iterations
IterNodes
done24
124
021

end0.0ms

sample1.2s

Algorithm
intervals
Results
712.0ms8000×body80valid
179.0ms8000×pre80true