Details

Time bar (total: 4.7s)

sample37.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify45.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- x y) (+ x y))
0.0b
(+ (* x x) (* y y))
19.8b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
10×add-exp-log add-cbrt-cube
8×frac-times flip3-+ flip-+ associate-/l/
7×add-cube-cbrt
6×flip3-- flip--
5×pow1 associate-*l* add-log-exp
4×associate-*r/ associate-*r* associate-*l/
3×times-frac associate-/r*
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 73
Calls
3 calls:
61.0ms
(* (- x y) (+ x y))
10.0ms
(+ (* x x) (* y y))
32.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series176.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(* (- x y) (+ x y))
29.0ms
(+ (* x x) (* y y))
82.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify73.0ms

Counts
82 → 82

prune226.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x y) (+ x y))
0.0b
(+ (* x x) (* y y))
0.0b
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
19.8b
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
41×associate-/r/
36×add-sqr-sqrt *-un-lft-identity
32×add-exp-log add-cube-cbrt
24×frac-times
20×flip3-+ add-cbrt-cube flip-+
18×flip3-- flip--
16×associate-/r*
14×div-exp
12×associate-*r/ associate-*l/
7×pow1 cbrt-undiv
6×div-inv associate-/l* add-log-exp
5×associate-*l* prod-exp
4×associate-*r*
3×rec-exp 1-exp cbrt-unprod
2×frac-2neg clear-num associate-/l/
1×+-commutative distribute-rgt-in pow-flip distribute-lft-in pow-prod-down sum-log *-commutative distribute-lft-out distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 161
Calls
4 calls:
49.0ms
(* (- x y) (+ x y))
17.0ms
(+ (* x x) (* y y))
68.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
70.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (- x y) (+ x y))
29.0ms
(+ (* x x) (* y y))
70.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
68.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify83.0ms

Counts
173 → 173

prune469.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (* (- x y) x) (* (- x y) y))
0.0b
(* (- x y) y)
19.8b
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×associate-*l/
17×*-un-lft-identity
15×add-cube-cbrt
12×times-frac
9×flip3-- flip--
8×add-exp-log frac-add add-cbrt-cube add-log-exp
6×pow1 associate-/l/
5×associate-*l* distribute-lft-out
4×flip3-+ flip-+ associate-/l*
3×associate-*r* associate-/r*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 88
Calls
4 calls:
13.0ms
(+ (* x x) (* y y))
32.0ms
(+ (* (- x y) x) (* (- x y) y))
29.0ms
(* (- x y) y)
57.0ms
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* x x) (* y y))
34.0ms
(+ (* (- x y) x) (* (- x y) y))
41.0ms
(* (- x y) y)
82.0ms
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

simplify95.0ms

Counts
100 → 100

prune390.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x y) x) (* (- x y) y))
0.0b
(log (exp (/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))))
0.0b
(* (- x y) y)
19.8b
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt times-frac
19×log-pow
18×exp-prod associate-*l/
9×flip3-- flip--
8×add-exp-log frac-add add-cbrt-cube distribute-lft-out
7×pow1
6×associate-/l/ add-log-exp
5×associate-*l*
4×flip3-+ associate-/r/ flip-+ associate-/l*
3×log-prod associate-*r* associate-/r*
2×div-inv
1×cbrt-undiv +-commutative frac-2neg div-exp rem-log-exp pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 107
Calls
4 calls:
32.0ms
(+ (* (- x y) x) (* (- x y) y))
95.0ms
(log (exp (/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))))
35.0ms
(* (- x y) y)
87.0ms
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* (- x y) x) (* (- x y) y))
74.0ms
(log (exp (/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))))
41.0ms
(* (- x y) y)
64.0ms
(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

simplify63.0ms

Counts
119 → 119

prune378.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes127.0ms

Accuracy

77.4% (4.5b remaining)

Error of 5.0b against oracle of 0.4b and baseline of 20.5b

bsearch112.0ms

Steps
ItersRangePoint
6
7.57387563408003e-178
3.856205723104632e-177
3.81890050297606e-177
8
-7.653706237395124e-160
-1.7669547785881474e-162
-8.743307936790759e-162
10
-4.868209042395978e+158
-1.1489753180495791e+148
-5.3752784922532734e+150

simplify49.0ms

end0.0ms

sample984.0ms

Algorithm
intervals
Results
527.0ms8000×body80valid
204.0ms8000×pre80true