Details

Time bar (total: 42.2s)

sample76.0ms

Algorithm
intervals
Results
42.0ms256×body80valid
11.0ms256×pre80true

simplify355.0ms

Counts
1 → 1
Iterations
IterNodes
done2000
3641
2119
136
015

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite881.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
3 → 453
Calls
3 calls:
291.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
384.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
190.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series465.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
194.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
90.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify970.0ms

Counts
462 → 462
Iterations
IterNodes
done2006
11387
0582

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.3b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
484×times-frac
370×*-un-lft-identity
302×sqrt-prod
284×add-sqr-sqrt
224×add-cube-cbrt
83×swap-sqr
64×distribute-lft-out
63×associate-*r* associate-*l*
38×associate-/r/
21×flip3-+ flip-+
19×pow1 div-inv
16×unswap-sqr
15×add-cbrt-cube add-exp-log
10×associate-/r*
9×associate-/l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/l/
5×pow-prod-up
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down pow-sqr
2×frac-times associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Counts
4 → 355
Calls
4 calls:
200.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
634.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
260.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
253.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
137.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
88.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify842.0ms

Counts
367 → 367
Iterations
IterNodes
done2004
11070
0553

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.5b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
2.3b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
3718×times-frac
2278×*-un-lft-identity
1580×add-sqr-sqrt add-cube-cbrt
1263×sqrt-prod
349×distribute-lft-out
206×associate-/l*
128×associate-/r/
110×sqrt-div
72×div-inv
65×flip3-+ flip-+
44×add-exp-log
31×div-exp
29×add-cbrt-cube
23×associate-/r*
16×cbrt-undiv
6×1-exp
5×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×rec-exp
Counts
4 → 1628
Calls
4 calls:
384.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
175.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
385.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
229.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

series834.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
160.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
243.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
126.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

simplify2.3s

Counts
1640 → 1640
Iterations
IterNodes
done2000
01681

prune10.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

localize119.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
2.3b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2 1)))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite893.0ms

Algorithm
rewrite-expression-head
Rules
5083×times-frac
3036×*-un-lft-identity
2560×sqrt-prod
2160×add-sqr-sqrt
2158×add-cube-cbrt
439×distribute-lft-out
417×associate-/l*
112×associate-/r/
110×sqrt-div
66×div-inv
56×flip3-+ flip-+
37×add-exp-log
27×div-exp
22×add-cbrt-cube
12×cbrt-undiv
10×associate-/r*
6×pow1 1-exp
4×insert-posit16 add-log-exp
2×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 2062
Calls
4 calls:
185.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
380.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2 1)))
116.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
99.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series499.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
228.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2 1)))
64.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.7s

Counts
2074 → 2074
Iterations
IterNodes
done2026
02026

prune11.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 2.3b

regimes229.0ms

Accuracy

93.3% (0.2b remaining)

Error of 1.5b against oracle of 1.4b and baseline of 3.7b

bsearch3.0ms

simplify17.0ms

Iterations
IterNodes
done62
162
043

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s8000×body80valid
839.0ms8000×pre80true