Details

Time bar (total: 12.1s)

sample21.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
8.0ms
(+ (* x x) 1.0)
17.0ms
(/ x (+ (* x x) 1.0))

series169.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(+ (* x x) 1.0)
107.0ms
(/ x (+ (* x x) 1.0))

simplify867.0ms

Counts
51 → 51
Iterations

Useful iterations: 2 (213.0ms)

IterNodesCost
089580
1231503
21201450
done5000450

prune122.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 div-exp
8×prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u 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 → 162
Calls
4 calls:
14.0ms
(/ 1 (sqrt (fma x x 1.0)))
55.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
6.0ms
(sqrt (fma x x 1.0))
3.0ms
(sqrt (fma x x 1.0))

series402.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ 1 (sqrt (fma x x 1.0)))
115.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
58.0ms
(sqrt (fma x x 1.0))
84.0ms
(sqrt (fma x x 1.0))

simplify3.0s

Counts
174 → 174
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02092888
16222599
241562282
done50002280

prune560.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

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))))

rewrite461.0ms

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×expm1-log1p-u associate-*r* associate-/r* associate-/r/ log1p-expm1-u
3×associate-+r+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp sum-log *-commutative div-inv
1×+-commutative distribute-rgt-in associate-+r- sub-neg fma-def frac-2neg distribute-lft-in diff-log swap-sqr prod-diff associate-*l/ clear-num
Counts
4 → 164
Calls
4 calls:
58.0ms
(* (* x x) (* x x))
43.0ms
(/ x (+ (pow x 6) (pow 1.0 3)))
61.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
287.0ms
(* (/ x (+ (pow x 6) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (* x x) (* x x))
311.0ms
(/ x (+ (pow x 6) (pow 1.0 3)))
60.0ms
(+ (* (* 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))))

simplify582.0ms

Counts
176 → 176
Iterations

Useful iterations: done (574.0ms)

IterNodesCost
02213181
17942698
done50002254

prune673.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (pow x 5))
0.4b
(/ 1.0 (pow x 3))
19.6b
(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

rewrite467.0ms

Algorithm
rewrite-expression-head
Rules
909×times-frac
637×*-un-lft-identity
624×add-sqr-sqrt add-cube-cbrt
522×associate-+r+
520×prod-diff
150×unpow-prod-down
129×cube-prod
57×div-inv
50×sqr-pow
43×cube-mult unpow3
25×fma-def
19×associate-/r*
13×add-exp-log
8×add-log-exp
7×add-cbrt-cube
6×div-exp associate-/l*
4×distribute-lft-out
3×pow1 expm1-log1p-u frac-add log1p-expm1-u distribute-lft-out--
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num sum-log
1×+-commutative associate-+r- sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 683
Calls
3 calls:
8.0ms
(/ 1.0 (pow x 5))
19.0ms
(/ 1.0 (pow x 3))
354.0ms
(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

series223.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(/ 1.0 (pow x 5))
73.0ms
(/ 1.0 (pow x 3))
55.0ms
(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

simplify1.3s

Counts
692 → 692
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0104718731
1232915599
done500014491

prune1.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

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

bsearch121.0ms

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

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03065
14051
done4051

end0.0ms

sample471.0ms

Algorithm
intervals
Results
306.0ms8000×body80valid