Details

Time bar (total: 17.2s)

sample43.0ms

Algorithm
intervals
Results
23.0ms473×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (96.0ms)

IterNodesCost
011245
121245
252245
3171245
4493220
51844220
done5000220

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(- t (* z z))
0.0b
(fma 4.0 (* (- t (* z z)) y) (* x x))
5.2b
(* (- t (* z z)) y)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1 add-cbrt-cube add-exp-log add-log-exp
4×associate-*l*
3×expm1-log1p-u fma-neg associate-*r* prod-diff log1p-expm1-u
2×flip3-- associate-*l/ flip-- difference-of-squares
1×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
3 → 54
Calls
3 calls:
5.0ms
(- t (* z z))
0.0ms
(fma 4.0 (* (- t (* z z)) y) (* x x))
15.0ms
(* (- t (* z z)) y)

series201.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(- t (* z z))
103.0ms
(fma 4.0 (* (- t (* z z)) y) (* x x))
54.0ms
(* (- t (* z z)) y)

simplify993.0ms

Counts
63 → 63
Iterations

Useful iterations: done (986.0ms)

IterNodesCost
09314494
121512014
286211743
done500111583

prune528.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(- t (* z z))
0.0b
(fma x x (* 4.0 (* (- t (* z z)) y)))
0.0b
(* 4.0 (* (- t (* z z)) y))
5.2b
(* (- t (* z z)) y)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×associate-*l*
6×add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- fma-neg prod-diff flip--
2×associate-*r/ *-commutative difference-of-squares
1×sub-neg diff-log fma-udef unswap-sqr
Counts
4 → 76
Calls
4 calls:
9.0ms
(- t (* z z))
1.0ms
(fma x x (* 4.0 (* (- t (* z z)) y)))
42.0ms
(* 4.0 (* (- t (* z z)) y))
19.0ms
(* (- t (* z z)) y)

series251.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- t (* z z))
89.0ms
(fma x x (* 4.0 (* (- t (* z z)) y)))
69.0ms
(* 4.0 (* (- t (* z z)) y))
50.0ms
(* (- t (* z z)) y)

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.1s)

IterNodesCost
011620929
128017305
2112516924
done500116634

prune603.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* (- t (* z z)) y)))
0.5b
(* (cbrt 4.0) (* (- t (* z z)) y))
1.0b
(* (cbrt 4.0) (cbrt 4.0))
5.2b
(* (- t (* z z)) y)

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
39×pow1
34×add-exp-log
27×add-sqr-sqrt
21×pow-prod-down
20×add-cbrt-cube prod-exp cbrt-unprod
19×cbrt-prod
17×associate-*l*
16×*-un-lft-identity add-cube-cbrt
11×associate-*r*
6×pow1/3 swap-sqr associate-*l/ associate-*r/
5×unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×flip3-- flip--
2×pow-sqr pow-prod-up
1×pow2 pow-plus difference-of-squares
Counts
4 → 122
Calls
4 calls:
105.0ms
(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* (- t (* z z)) y)))
34.0ms
(* (cbrt 4.0) (* (- t (* z z)) y))
27.0ms
(* (cbrt 4.0) (cbrt 4.0))
29.0ms
(* (- t (* z z)) y)

series496.0ms

Counts
4 → 10
Calls
4 calls:
234.0ms
(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* (- t (* z z)) y)))
171.0ms
(* (cbrt 4.0) (* (- t (* z z)) y))
0.0ms
(* (cbrt 4.0) (cbrt 4.0))
90.0ms
(* (- t (* z z)) y)

simplify2.0s

Counts
132 → 132
Iterations

Useful iterations: done (2.0s)

IterNodesCost
014736462
140032388
2229031988
done500026908

prune796.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x x (* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y))))
0.3b
(* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y)))
0.5b
(* (cbrt 4.0) (* (- t (* z z)) y))
5.2b
(* (- t (* z z)) y)

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1 add-exp-log
36×add-cbrt-cube
31×pow-prod-down prod-exp cbrt-unprod
11×add-sqr-sqrt associate-*l*
8×*-un-lft-identity add-cube-cbrt
6×associate-*l/ associate-*r/
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod flip3-- *-commutative flip--
1×fma-udef difference-of-squares unswap-sqr
Counts
4 → 99
Calls
4 calls:
1.0ms
(fma x x (* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y))))
250.0ms
(* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y)))
24.0ms
(* (cbrt 4.0) (* (- t (* z z)) y))
15.0ms
(* (- t (* z z)) y)

series716.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(fma x x (* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y))))
199.0ms
(* (* (* (cbrt 4.0) (sqrt (cbrt 4.0))) (sqrt (cbrt 4.0))) (* (cbrt 4.0) (* (- t (* z z)) y)))
216.0ms
(* (cbrt 4.0) (* (- t (* z z)) y))
61.0ms
(* (- t (* z z)) y)

simplify2.1s

Counts
111 → 111
Iterations

Useful iterations: done (2.1s)

IterNodesCost
015042625
143133652
2230633062
done500024612

prune719.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.4b

regimes934.0ms

Accuracy

70.8% (1.0b remaining)

Error of 3.7b against oracle of 2.7b and baseline of 6.0b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
020646
126646
done26646

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s16134×body80valid