Details

Time bar (total: 4.8s)

sample52.0ms

Algorithm
intervals
Results
26.0ms436×body80valid

simplify47.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize329.0ms

Local error

Found 2 expressions with local error:

3.8b
(- (+ (* x x) (* y y)) (* z z))
28.5b
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
add-exp-log add-sqr-sqrt add-cbrt-cube add-log-exp
add-cube-cbrt *-un-lft-identity times-frac associate-/l*
difference-of-squares
pow1 cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l/
sub-neg frac-2neg div-sub prod-exp associate--l+ clear-num associate-/r* sum-log cbrt-unprod div-inv
Counts
2 → 41
Calls
2 calls:
60.0ms
(- (+ (* x x) (* y y)) (* z z))
100.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series146.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(- (+ (* x x) (* y y)) (* z z))
95.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify30.0ms

Counts
47 → 47

prune143.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
7.5b
(/ (pow x 2) y)
8.9b
(/ (pow z 2) y)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
39×*-un-lft-identity
37×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
16×associate-/l*
13×add-exp-log
unpow2 sqr-pow
add-cbrt-cube
div-exp associate-/r*
add-log-exp
pow1
cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
+-commutative flip3-+ sum-log flip-+ distribute-lft-out
Counts
3 → 110
Calls
3 calls:
27.0ms
(+ y (/ (pow x 2) y))
14.0ms
(/ (pow x 2) y)
17.0ms
(/ (pow z 2) y)

series85.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ y (/ (pow x 2) y))
27.0ms
(/ (pow x 2) y)
25.0ms
(/ (pow z 2) y)

simplify74.0ms

Counts
119 → 119

prune357.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.1b
(/ (pow x (/ 2 2)) (/ y x))
8.9b
(/ (pow z 2) y)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
106×*-un-lft-identity
104×add-sqr-sqrt add-cube-cbrt
54×unpow-prod-down
21×add-exp-log
18×sqr-pow
16×associate-/r*
15×associate-/l*
12×div-exp
10×add-cbrt-cube div-inv
add-log-exp
cbrt-undiv unpow2
pow1 pow-to-exp pow-exp
frac-2neg clear-num
+-commutative flip3-+ sum-log associate-/r/ flip-+ distribute-lft-out
Counts
3 → 191
Calls
3 calls:
37.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
20.0ms
(/ (pow x (/ 2 2)) (/ y x))
9.0ms
(/ (pow z 2) y)

series94.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
28.0ms
(/ (pow x (/ 2 2)) (/ y x))
29.0ms
(/ (pow z 2) y)

simplify83.0ms

Counts
200 → 200

prune517.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.1b
(/ (pow x (/ 2 2)) (/ y x))
0.2b
(* z (/ z y))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
100×add-sqr-sqrt
97×*-un-lft-identity
95×add-cube-cbrt
42×unpow-prod-down
21×add-exp-log
14×sqr-pow
13×associate-*r* associate-/r* add-cbrt-cube
10×div-exp div-inv
associate-/l*
pow1 add-log-exp
cbrt-undiv
associate-*l*
pow-to-exp pow-exp prod-exp cbrt-unprod unswap-sqr
+-commutative frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num sum-log associate-/r/ *-commutative flip-+ distribute-lft-out
Counts
3 → 174
Calls
3 calls:
44.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
20.0ms
(/ (pow x (/ 2 2)) (/ y x))
20.0ms
(* z (/ z y))

series75.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
21.0ms
(/ (pow x (/ 2 2)) (/ y x))
20.0ms
(* z (/ z y))

simplify73.0ms

Counts
183 → 183

prune440.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes105.0ms

Accuracy

-13344.5% (12.2b remaining)

Error of 12.3b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify100.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.0s13724×body80valid