Details

Time bar (total: 3.6s)

sample17.0ms

Algorithm
intervals
Results
6.0ms336×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1263
2623
31643
43203
54383
66003
78313
814513
923573
1025453
1125453
done25453

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ x y) (- 1.0 z))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
18×prod-diff
15×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
5×associate-*r*
4×frac-times associate-*l*
3×pow1 add-exp-log flip3-- flip3-+ add-cbrt-cube flip-- flip-+
2×sub-neg associate-*r/ associate-*l/
1×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u distribute-lft-out distribute-lft-out-- add-log-exp difference-of-squares unswap-sqr
Counts
1 → 53
Calls
1 calls:
35.0ms
(* (+ x y) (- 1.0 z))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(* (+ x y) (- 1.0 z))

simplify45.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0397499
11589357
25001356
done5001356

prune83.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* z z) (* 1.0 z))
0.5b
(* (+ x y) (- (pow 1.0 3) (pow z 3)))
15.7b
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
288×prod-diff
177×add-sqr-sqrt
163×*-un-lft-identity
156×unpow-prod-down cube-prod
151×add-cube-cbrt
146×distribute-rgt-in distribute-lft-in
56×sqr-pow
48×cube-mult unpow3
25×associate-*r*
16×difference-of-squares
10×add-exp-log add-cbrt-cube
8×frac-times flip3-+ flip-+ associate-/l/
6×flip3-- flip--
5×pow1 distribute-lft-out-- add-log-exp
4×associate-*r/ associate-*l* associate-*l/
3×expm1-log1p-u times-frac associate-/r* log1p-expm1-u
2×cbrt-undiv sub-neg div-exp prod-exp associate-/r/ cbrt-unprod
1×difference-cubes +-commutative distribute-rgt-out fma-def frac-2neg pow-prod-down clear-num sum-log *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 391
Calls
3 calls:
8.0ms
(+ (* z z) (* 1.0 z))
115.0ms
(* (+ x y) (- (pow 1.0 3) (pow z 3)))
123.0ms
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))

series302.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ (* z z) (* 1.0 z))
106.0ms
(* (+ x y) (- (pow 1.0 3) (pow z 3)))
143.0ms
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))

simplify80.0ms

Counts
400 → 400
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016375395
150014040
done50014040

prune333.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))
8.6b
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
8.6b
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
11.2b
(/ (/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
72×sqrt-prod
61×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
22×sqrt-div
18×add-exp-log associate-/r/ add-cbrt-cube
14×flip3-+ flip-+
13×associate-/l*
12×associate-/r*
9×div-inv associate-/l/
7×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×flip3-- flip--
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod hypot-def
Counts
4 → 186
Calls
4 calls:
122.0ms
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))
28.0ms
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
29.0ms
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
106.0ms
(/ (/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))
48.0ms
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
46.0ms
(sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))
139.0ms
(/ (/ (* (+ x y) (- (pow 1.0 3) (pow z 3))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z))))) (sqrt (+ (* 1.0 1.0) (+ (* z z) (* 1.0 z)))))

simplify103.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08034390
137033922
250013919
done50013919

prune602.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x z (* z y))
0.0b
(fma 1.0 y (- (fma x z (* z y))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma x z (* z y))
0.0ms
(fma 1.0 y (- (fma x z (* z y))))

series78.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(fma x z (* z y))
41.0ms
(fma 1.0 y (- (fma x z (* z y))))

simplify65.0ms

Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
042116
1113102
2436102
32118102
45002102
done5002102

prune57.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes140.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.7b

bsearch65.0ms

Steps
ItersRangePoint
8
49821777349.62285
16596154459827.314
511536835406.9681
6
-12803139111072366.0
-1018566962106419.2
-1324274292343200.2

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03723
13723
done3723

end0.0ms

sample443.0ms

Algorithm
intervals
Results
181.0ms10108×body80valid
0.0ms1×body1280valid