Details

Time bar (total: 3.1m)

sample72.0ms

Algorithm
intervals
Results
43.0ms256×body80valid
11.0ms256×pre80true

simplify1.4s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize36.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
0.0b
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ 1.0 (+ beta (fma beta alpha alpha)))

rewrite528.0ms

Algorithm
rewrite-expression-head
Rules
5704×*-un-lft-identity
3256×times-frac
2988×distribute-lft-out
886×add-sqr-sqrt add-cube-cbrt
197×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num sum-log fma-def frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1441
Calls
4 calls:
Slowest
224.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
118.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
67.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
11.0ms
(+ 1.0 (+ beta (fma beta alpha alpha)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
198.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
136.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
31.0ms
(+ 1.0 (+ beta (fma beta alpha alpha)))

simplify1.5s

Counts
2600 → 1453

prune16.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize61.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
3.9b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
0.1b
(* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
11512×*-un-lft-identity
7123×times-frac
5934×distribute-lft-out
2633×sqrt-prod
2134×add-sqr-sqrt
1931×add-cube-cbrt
990×associate-*r*
496×associate-*l*
200×associate-/r/
174×associate-/l*
102×flip3-+ flip-+
101×div-inv
45×unswap-sqr
27×add-exp-log
22×add-cbrt-cube
16×associate-/r*
10×div-exp
7×cbrt-undiv
6×pow1 prod-exp
5×associate-/l/
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×1-exp
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2836
Calls
4 calls:
Slowest
1.3s
(* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
189.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
97.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
61.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
167.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
103.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
98.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify6.7s

Counts
3930 → 2848

prune45.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
0.0b
(/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ 1.0 (+ beta alpha))

rewrite546.0ms

Algorithm
rewrite-expression-head
Rules
5704×*-un-lft-identity
3256×times-frac
2988×distribute-lft-out
886×add-sqr-sqrt add-cube-cbrt
197×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num sum-log fma-def frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1441
Calls
4 calls:
Slowest
233.0ms
(/ (/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
123.0ms
(/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
81.0ms
(/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha)))
12.0ms
(+ 1.0 (+ beta alpha))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
107.0ms
(/ (/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
71.0ms
(/ (+ 1.0 (+ beta alpha)) (+ 2 (+ beta alpha)))
19.0ms
(+ 1.0 (+ beta alpha))

simplify1.7s

Counts
2600 → 1453

prune14.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
0.6b
(/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 2 (+ beta alpha)) 1.0)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
15370×*-un-lft-identity
11279×times-frac
7308×distribute-lft-out
4475×cbrt-prod
3565×add-sqr-sqrt add-cube-cbrt
2645×sqrt-prod
489×associate-/l*
216×associate-/r/
130×div-inv
110×flip3-+ flip-+
80×add-exp-log
48×div-exp
40×add-cbrt-cube
32×cbrt-undiv
28×sqrt-div
26×associate-/r*
14×cbrt-div
12×prod-exp
7×cbrt-unprod
6×1-exp
4×expm1-log1p-u frac-times pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×associate-*l/ associate-*r/
Counts
4 → 4475
Calls
4 calls:
Slowest
326.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 2 (+ beta alpha)) 1.0)))
162.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
90.0ms
(/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
81.0ms
(/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
526.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
461.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (cbrt (+ (+ 2 (+ beta alpha)) 1.0)))
297.0ms
(/ (/ (cbrt (+ 1.0 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
264.0ms
(/ (/ (* (cbrt (+ 1.0 (+ beta alpha))) (cbrt (+ 1.0 (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha))))

simplify8.9s

Counts
8343 → 4487

prune1.3m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes202.0ms

Accuracy

53.1% (1.2b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.8b

bsearch39.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
313.0ms8000×pre80true