Details

Time bar (total: 22.6s)

sample37.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
10.0ms256×pre80true

simplify7.1s

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
0915
12314
25214
311314
422914
546114
682214
7130814
8329614
done500014

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (- x y) (+ x y))
18.1b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
8×frac-times associate-/l/
7×flip3-+ flip-+
6×add-cube-cbrt flip3-- flip--
5×associate-*l*
4×pow1 associate-*r/ associate-*r* associate-*l/
3×times-frac associate-/r*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
2 → 66
Calls
2 calls:
40.0ms
(* (- x y) (+ x y))
38.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series138.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(* (- x y) (+ x y))
94.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.9s

Counts
72 → 72
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01231120
13921018
22015894
done5001886

prune231.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x y)
0.0b
(/ (+ x y) (hypot x y))
0.0b
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
0.0b
(/ (- x y) (hypot x y))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*l*
16×associate-*r*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp unswap-sqr
2×frac-2neg clear-num
1×frac-times hypot-udef flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 146
Calls
4 calls:
1.0ms
(hypot x y)
39.0ms
(/ (+ x y) (hypot x y))
107.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
22.0ms
(/ (- x y) (hypot x y))

series464.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(hypot x y)
113.0ms
(/ (+ x y) (hypot x y))
160.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
122.0ms
(/ (- x y) (hypot x y))

simplify1.6s

Counts
158 → 158
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01722247
14792185
216421971
done50011970

prune537.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (cbrt (/ (- x y) (hypot x y))) (cbrt (/ (- x y) (hypot x y)))) (cbrt (/ (- x y) (hypot x y))))
0.0b
(cbrt (/ (- x y) (hypot x y)))
0.0b
(cbrt (/ (- x y) (hypot x y)))
0.0b
(cbrt (/ (- x y) (hypot x y)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
78×cbrt-prod
69×add-sqr-sqrt
65×*-un-lft-identity
61×times-frac
41×add-cube-cbrt
23×pow1
22×associate-*r*
15×cbrt-div
12×pow1/3 distribute-lft-out-- difference-of-squares
9×add-exp-log pow-prod-up
6×pow-plus
5×frac-times pow-prod-down associate-*l/ add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ prod-exp pow-sqr cbrt-unprod unswap-sqr
2×pow2
1×associate-*l* pow3 *-commutative
Counts
4 → 151
Calls
4 calls:
106.0ms
(* (* (cbrt (/ (- x y) (hypot x y))) (cbrt (/ (- x y) (hypot x y)))) (cbrt (/ (- x y) (hypot x y))))
6.0ms
(cbrt (/ (- x y) (hypot x y)))
5.0ms
(cbrt (/ (- x y) (hypot x y)))
6.0ms
(cbrt (/ (- x y) (hypot x y)))

series1.1s

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (* (cbrt (/ (- x y) (hypot x y))) (cbrt (/ (- x y) (hypot x y)))) (cbrt (/ (- x y) (hypot x y))))
336.0ms
(cbrt (/ (- x y) (hypot x y)))
343.0ms
(cbrt (/ (- x y) (hypot x y)))
303.0ms
(cbrt (/ (- x y) (hypot x y)))

simplify3.8s

Counts
163 → 163
Iterations

Useful iterations: 3 (399.0ms)

IterNodesCost
01382970
12832847
26312463
311562388
445212388
done50012388

prune584.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (/ (+ x y) (hypot x y)))
0.0b
(cbrt (/ (+ x y) (hypot x y)))
0.0b
(cbrt (/ (+ x y) (hypot x y)))
0.0b
(* (cbrt (/ (+ x y) (hypot x y))) (cbrt (/ (+ x y) (hypot x y))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
136×cbrt-prod
128×*-un-lft-identity
102×times-frac
92×add-sqr-sqrt
68×add-cube-cbrt
27×distribute-lft-out
25×swap-sqr
19×associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 176
Calls
4 calls:
5.0ms
(cbrt (/ (+ x y) (hypot x y)))
5.0ms
(cbrt (/ (+ x y) (hypot x y)))
5.0ms
(cbrt (/ (+ x y) (hypot x y)))
58.0ms
(* (cbrt (/ (+ x y) (hypot x y))) (cbrt (/ (+ x y) (hypot x y))))

series732.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(cbrt (/ (+ x y) (hypot x y)))
181.0ms
(cbrt (/ (+ x y) (hypot x y)))
183.0ms
(cbrt (/ (+ x y) (hypot x y)))
175.0ms
(* (cbrt (/ (+ x y) (hypot x y))) (cbrt (/ (+ x y) (hypot x y))))

simplify2.0s

Counts
188 → 188
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01363614
11973429
25143315
38513118
419293108
done50003045

prune689.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01134
11434
done1434

end0.0ms

sample1.2s

Algorithm
intervals
Results
471.0ms8000×pre80true
440.0ms8000×body80valid