Details

Time bar (total: 50.7s)

sample128.0ms

Algorithm
intervals
Results
89.0ms479×body80valid

simplify6.6s

Counts
1 → 1
Iterations
IterNodes
done5000
43892
3995
2247
170
028

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize191.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite3.8s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 163
Calls
4 calls:
1.2s
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.4s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
117.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
3.0ms
(sqrt PI)

series995.0ms

Counts
4 → 10
Calls
4 calls:
133.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
782.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
79.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.8s

Counts
173 → 173
Iterations
IterNodes
done5000
11200
0350

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))
0.1b
(fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (sqrt (/ 1 PI)) (* (fma 0.6666666666666666 (* (* (fabs x) (fabs x)) (fabs x)) (fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))) 1.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
28×pow1
17×associate-*l*
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity sqrt-prod
9×times-frac
6×pow-plus pow-prod-down prod-exp pow-prod-up cbrt-unprod
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×pow2 pow-sqr *-commutative fma-udef
1×sqrt-div pow3 associate-*l/ div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
1.0ms
(fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))
1.0ms
(fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))
38.0ms
(* (* (fabs x) (fabs x)) (fabs x))
62.0ms
(* (sqrt (/ 1 PI)) (* (fma 0.6666666666666666 (* (* (fabs x) (fabs x)) (fabs x)) (fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
260.0ms
(fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))
169.0ms
(fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))
44.0ms
(* (* (fabs x) (fabs x)) (fabs x))
586.0ms
(* (sqrt (/ 1 PI)) (* (fma 0.6666666666666666 (* (* (fabs x) (fabs x)) (fabs x)) (fma (pow (fabs x) 5) 0.2 (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))) 1.0))

simplify3.5s

Counts
96 → 96
Iterations
IterNodes
done5002
21096
1314
0146

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize178.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(* (cbrt PI) (cbrt PI))
1.0b
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b
(sqrt (* (cbrt PI) (cbrt PI)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×add-cube-cbrt *-un-lft-identity
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up add-cbrt-cube
5×sqrt-prod
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp unswap-sqr
3×pow2 pow-plus associate-/l*
2×pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp frac-2neg 1-exp prod-exp clear-num *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 123
Calls
4 calls:
1.0ms
(cbrt PI)
19.0ms
(* (cbrt PI) (cbrt PI))
30.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
14.0ms
(sqrt (* (cbrt PI) (cbrt PI)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(* (cbrt PI) (cbrt PI))
0.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms
(sqrt (* (cbrt PI) (cbrt PI)))

simplify4.0s

Counts
127 → 127
Iterations
IterNodes
done5000
31474
2558
1264
0139

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1.0 (fabs (cbrt PI))) (/ (sqrt (cbrt PI)) (fma (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0) (fabs x) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))))
1.0b
(/ 1.0 (fabs (cbrt PI)))
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
1078×times-frac
504×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
252×sqrt-prod
132×cbrt-prod
48×div-inv
34×associate-/r*
18×add-exp-log add-cbrt-cube
16×associate-/l*
9×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg pow1/3 clear-num
1×associate-/r/ associate-/l/
Counts
4 → 524
Calls
4 calls:
50.0ms
(/ (/ 1.0 (fabs (cbrt PI))) (/ (sqrt (cbrt PI)) (fma (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0) (fabs x) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))))
8.0ms
(/ 1.0 (fabs (cbrt PI)))
1.0ms
(cbrt PI)
2.0ms
(cbrt PI)

series1.1s

Counts
4 → 6
Calls
4 calls:
1.1s
(/ (/ 1.0 (fabs (cbrt PI))) (/ (sqrt (cbrt PI)) (fma (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0) (fabs x) (* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x)) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))))
0.0ms
(/ 1.0 (fabs (cbrt PI)))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify6.5s

Counts
530 → 530
Iterations
IterNodes
done5000
12651
0801

prune7.6s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes785.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done30
130
024

end0.0ms

sample5.4s

Algorithm
intervals
Results
5.0s13905×body80valid