Details

Time bar (total: 20.8s)

sample92.0ms

Algorithm
intervals
Results
69.0ms440×body80valid

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5001
31049
2250
170
028

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
33×add-cbrt-cube add-exp-log
31×add-sqr-sqrt
28×times-frac
26×*-un-lft-identity add-cube-cbrt
24×associate-*l*
20×pow1
17×associate-*r*
15×prod-exp cbrt-unprod
12×sqrt-prod
9×pow-prod-down
5×distribute-rgt-in distribute-lft-in associate-*r/
4×expm1-log1p-u cbrt-undiv div-exp fma-udef log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
2×div-inv
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l/ frac-add flip-+
Counts
4 → 126
Calls
4 calls:
27.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0)))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
62.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0))))
34.0ms
(* (* (fabs x) (fabs x)) (/ 1.0 21.0))
2.0ms
(sqrt PI)

series560.0ms

Counts
4 → 10
Calls
4 calls:
424.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0)))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
84.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (* (* (fabs x) (fabs x)) (/ 1.0 21.0))))
52.0ms
(* (* (fabs x) (fabs x)) (/ 1.0 21.0))
0.0ms
(sqrt PI)

simplify1.6s

Counts
136 → 136
Iterations
IterNodes
done5001
1759
0242

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
23×add-sqr-sqrt *-un-lft-identity associate-*l*
21×times-frac add-cube-cbrt
15×pow1
12×prod-exp sqrt-prod cbrt-unprod
6×pow-prod-down
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp associate-*r*
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-/r* associate-*r/
2×*-commutative div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*l/ frac-add flip-+ distribute-lft-out associate-/l* unswap-sqr
Counts
4 → 115
Calls
4 calls:
44.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
34.0ms
(/ (* (* (fabs x) (fabs x)) 1.0) 21.0)
132.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0)))
2.0ms
(sqrt PI)

series486.0ms

Counts
4 → 10
Calls
4 calls:
365.0ms
(* (/ 1.0 (sqrt PI)) (* (fabs x) (fma (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0))) (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) 2.0))))
40.0ms
(/ (* (* (fabs x) (fabs x)) 1.0) 21.0)
81.0ms
(* (* (fabs x) (fabs x)) (+ (/ 1.0 5.0) (/ (* (* (fabs x) (fabs x)) 1.0) 21.0)))
0.0ms
(sqrt PI)

simplify3.2s

Counts
125 → 125
Iterations
IterNodes
done5000
24889
1691
0227

prune961.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
401×pow1
157×pow-prod-up
107×pow-prod-down
69×add-cbrt-cube add-exp-log
53×pow-sqr
46×prod-exp cbrt-unprod
40×pow-plus
29×pow2
15×cube-unmult
6×add-sqr-sqrt associate-*l*
5×*-un-lft-identity add-cube-cbrt
4×distribute-rgt-in expm1-log1p-u distribute-lft-in associate-*r* *-commutative fma-udef log1p-expm1-u add-log-exp
2×swap-sqr unswap-sqr
1×sqrt-div associate-*l/ associate-*r/
Counts
4 → 221
Calls
4 calls:
24.0ms
(* (fabs x) (* (fabs x) (fabs x)))
69.0ms
(* (* 1.0 (fabs x)) (* (sqrt (/ 1 PI)) (fma (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (* (fabs x) (fabs x)))) 0.047619047619047616 (fma 0.2 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 0.6666666666666666 (* (fabs x) (fabs x)) 2.0)))))
109.0ms
(* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (* (fabs x) (fabs x))))
23.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))

series546.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (fabs x) (* (fabs x) (fabs x)))
401.0ms
(* (* 1.0 (fabs x)) (* (sqrt (/ 1 PI)) (fma (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (* (fabs x) (fabs x)))) 0.047619047619047616 (fma 0.2 (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 0.6666666666666666 (* (fabs x) (fabs x)) 2.0)))))
55.0ms
(* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (* (fabs x) (fabs x))))
38.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))

simplify1.7s

Counts
233 → 233
Iterations
IterNodes
done5000
1668
0198

prune812.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×*-un-lft-identity add-cube-cbrt
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×add-cbrt-cube swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up
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 clear-num frac-2neg 1-exp prod-exp *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 123
Calls
4 calls:
1.0ms
(cbrt PI)
22.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
10.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
17.0ms
(* (cbrt PI) (cbrt PI))

series0.0ms

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

simplify1.3s

Counts
127 → 127
Iterations
IterNodes
done5000
2945
1259
0134

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes408.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done28
128
022

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.3s14022×body80valid