Details

Time bar (total: 56.8s)

sample145.0ms

Algorithm
intervals
Results
111.0ms442×body80valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5001
31966
2271
175
028

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize112.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite10.8s

Algorithm
rewrite-expression-head
Rules
181×add-exp-log
128×prod-exp
107×add-cbrt-cube
70×cbrt-unprod
51×pow1
48×associate-*l*
46×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity pow-prod-down
33×add-cube-cbrt
19×div-exp
15×associate-*l/
14×sqrt-prod
12×frac-add
11×cbrt-undiv
8×rec-exp 1-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 195
Calls
4 calls:
8.8s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.9s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series485.0ms

Counts
4 → 10
Calls
4 calls:
110.0ms
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
322.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
52.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.3s

Counts
205 → 205
Iterations
IterNodes
done5000
11471
0400

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize106.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)
7.0b
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
7.0b
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))

rewrite17.8s

Algorithm
rewrite-expression-head
Rules
86×pow1
62×pow-prod-down
25×add-cbrt-cube add-exp-log
17×sqrt-pow1
13×add-sqr-sqrt associate-*l*
12×*-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
9×times-frac
5×sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow1/2 div-exp associate-*l/
2×sqrt-div
1×rem-sqrt-square associate-*r* *-commutative div-inv
Counts
4 → 99
Calls
4 calls:
56.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)
8.8s
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
8.9s
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))

series309.0ms

Counts
4 → 10
Calls
4 calls:
55.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)
130.0ms
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
123.0ms
(sqrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))

simplify1.2s

Counts
109 → 109
Iterations
IterNodes
done5001
21010
1307
0129

prune881.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite4.3s

Algorithm
rewrite-expression-head
Rules
62×pow1
43×add-exp-log
40×add-sqr-sqrt
39×add-cbrt-cube
38×associate-*l/
36×associate-*l* frac-add
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
22×frac-times prod-exp associate-*r/
21×pow-plus pow-prod-up
20×cbrt-unprod
14×flip3-+ sqrt-prod flip-+
13×pow-prod-down
7×associate-*r*
5×div-exp unswap-sqr
4×pow2 expm1-log1p-u cbrt-undiv pow-sqr insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow3 div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp
Counts
4 → 178
Calls
4 calls:
46.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
4.2s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
88.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series675.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
568.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
74.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.1s

Counts
188 → 188
Iterations
IterNodes
done5000
11316
0355

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 7) 21)
0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.1b
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21)))))
0.1b
(fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
32×times-frac
31×*-un-lft-identity
30×add-cube-cbrt
20×pow1
19×associate-*l*
16×add-exp-log sqrt-prod
13×add-cbrt-cube
12×unpow-prod-down
7×associate-/l*
5×pow-prod-up unswap-sqr
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×associate-/r* div-exp fma-udef
2×*-commutative div-inv
1×pow2 distribute-rgt-in pow-to-exp cbrt-undiv clear-num frac-2neg distribute-lft-in pow-plus sqrt-div cube-unmult associate-*l/ pow-exp pow-sqr
Counts
4 → 126
Calls
4 calls:
10.0ms
(/ (pow (fabs x) 7) 21)
28.0ms
(* (fabs x) (* (fabs x) (fabs x)))
11.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21)))))
0.0ms
(fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21))

series600.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (pow (fabs x) 7) 21)
36.0ms
(* (fabs x) (* (fabs x) (fabs x)))
338.0ms
(* (sqrt (/ 1 PI)) (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21)))))
147.0ms
(fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (/ (pow (fabs x) 7) 21))

simplify1.6s

Counts
138 → 138
Iterations
IterNodes
done5001
21669
1425
0220

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes100.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
done31
131
026

end0.0ms

sample5.8s

Algorithm
intervals
Results
5.5s14180×body80valid