Details

Time bar (total: 12.2s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
167
done67

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) 1.0)
14.5b
(/ x (+ (* x x) 1.0))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 40
Calls
2 calls:
12.0ms
(+ (* x x) 1.0)
26.0ms
(/ x (+ (* x x) 1.0))

series127.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(+ (* x x) 1.0)
79.0ms
(/ x (+ (* x x) 1.0))

simplify908.0ms

Counts
46 → 46
Iterations

Useful iterations: 2 (271.0ms)

IterNodesCost
085552
1224536
21231476
done5000476

prune132.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
14.5b
(sqrt (+ (* x x) 1.0))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 sqrt-div div-exp
8×prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 164
Calls
4 calls:
129.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
18.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
16.0ms
(sqrt (+ (* x x) 1.0))
19.0ms
(sqrt (+ (* x x) 1.0))

series369.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
116.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
85.0ms
(sqrt (+ (* x x) 1.0))
80.0ms
(sqrt (+ (* x x) 1.0))

simplify3.8s

Counts
176 → 176
Iterations

Useful iterations: done (3.8s)

IterNodesCost
02253329
16903023
243722647
done50012643

prune468.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x x))
2.0b
(/ x (+ (pow x 6) (pow 1.0 3)))
12.4b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
25.5b
(* (/ x (+ (pow x 6) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
36×*-un-lft-identity pow-prod-up
27×add-sqr-sqrt
25×times-frac
24×pow-prod-down
23×add-exp-log add-cbrt-cube
22×add-cube-cbrt pow-sqr
19×associate-*l*
18×pow-plus
13×pow2
10×prod-exp cbrt-unprod
9×add-log-exp
7×distribute-lft-out
5×flip3-+ flip-+
4×associate-*r* associate-/r* associate-/r/
3×associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-+r+ associate-*r/ div-exp sum-log *-commutative div-inv
1×+-commutative distribute-rgt-in associate-+r- sub-neg frac-2neg distribute-lft-in diff-log swap-sqr associate-*l/ clear-num
Counts
4 → 154
Calls
4 calls:
52.0ms
(* (* x x) (* x x))
56.0ms
(/ x (+ (pow x 6) (pow 1.0 3)))
57.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
316.0ms
(* (/ x (+ (pow x 6) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* x x) (* x x))
312.0ms
(/ x (+ (pow x 6) (pow 1.0 3)))
57.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
167.0ms
(* (/ x (+ (pow x 6) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

simplify574.0ms

Counts
166 → 166
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
02093036
17562637
done50012193

prune546.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 (pow x 5)) (/ 1 x))
0.2b
(/ 1.0 (pow x 5))
0.4b
(/ 1.0 (pow x 3))
19.5b
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

rewrite632.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
65×*-un-lft-identity
58×add-sqr-sqrt
45×add-cube-cbrt
25×unpow-prod-down
19×associate-/r*
14×add-exp-log
13×cube-prod
11×add-log-exp
9×sqr-pow
8×add-cbrt-cube
6×div-exp distribute-lft-out associate-/l*
5×difference-of-squares
4×pow1 cube-mult unpow3 div-inv distribute-lft-out--
3×frac-sub
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ diff-log frac-add pow-exp clear-num sum-log flip-+
1×+-commutative sub-neg flip3-- associate--l+ flip--
Counts
4 → 151
Calls
4 calls:
86.0ms
(+ (/ 1.0 (pow x 5)) (/ 1 x))
15.0ms
(/ 1.0 (pow x 5))
17.0ms
(/ 1.0 (pow x 3))
502.0ms
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(+ (/ 1.0 (pow x 5)) (/ 1 x))
87.0ms
(/ 1.0 (pow x 5))
77.0ms
(/ 1.0 (pow x 3))
79.0ms
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

simplify1.6s

Counts
163 → 163
Iterations

Useful iterations: 2 (592.0ms)

IterNodesCost
02292274
15212011
228131945
done50021945

prune465.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.3b

bsearch122.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
454.92579415143206
10
-2676750800.736259
-2.9526231381329305e-09
-64270072.71622895

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03065
14051
done4051

end0.0ms

sample526.0ms

Algorithm
intervals
Results
341.0ms8000×body80valid