Details

Time bar (total: 45.2s)

sample212.0ms

Algorithm
intervals
Results
123.0ms573×body80valid

simplify6.1s

Counts
1 → 1
Iterations
IterNodes
done5000
54998
42295
3723
2217
167
028

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
0.3b
(* 27.0 (* k j))
2.0b
(* (* t x) (* y 18.0))
6.4b
(* z (* (* t x) (* y 18.0)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
39×pow1 add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* prod-diff *-commutative
1×sub-neg flip3-- fma-neg diff-log fma-udef flip-- associate--r+
Counts
4 → 92
Calls
4 calls:
76.0ms
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
15.0ms
(* 27.0 (* k j))
28.0ms
(* (* t x) (* y 18.0))
92.0ms
(* z (* (* t x) (* y 18.0)))

series969.0ms

Counts
4 → 12
Calls
4 calls:
798.0ms
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
34.0ms
(* 27.0 (* k j))
47.0ms
(* (* t x) (* y 18.0))
90.0ms
(* z (* (* t x) (* y 18.0)))

simplify1.9s

Counts
104 → 104
Iterations
IterNodes
done5000
21667
1437
0177

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* (* 27.0 k) j)))
0.7b
(* (* 27.0 k) j)
2.0b
(* (* t x) (* y 18.0))
6.4b
(* z (* (* t x) (* y 18.0)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
39×pow1 add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
5×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×prod-diff *-commutative
1×sub-neg flip3-- fma-neg diff-log fma-udef flip-- associate--r+
Counts
4 → 92
Calls
4 calls:
66.0ms
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* (* 27.0 k) j)))
25.0ms
(* (* 27.0 k) j)
25.0ms
(* (* t x) (* y 18.0))
74.0ms
(* z (* (* t x) (* y 18.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
794.0ms
(- (* z (* (* t x) (* y 18.0))) (fma 4.0 (fma t a (* x i)) (* (* 27.0 k) j)))
43.0ms
(* (* 27.0 k) j)
74.0ms
(* (* t x) (* y 18.0))
115.0ms
(* z (* (* t x) (* y 18.0)))

simplify1.9s

Counts
104 → 104
Iterations
IterNodes
done5006
21740
1448
0179

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize228.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
2.0b
(* (* t x) (* y 18.0))
2.6b
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
62.0b
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-cbrt-cube add-exp-log
8×pow-prod-down prod-exp cbrt-unprod
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod
2×fma-udef
1×pow1/3 associate-*r* associate-*l* *-commutative
Counts
4 → 57
Calls
4 calls:
1.0ms
(cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
24.0ms
(* (* t x) (* y 18.0))
1.0ms
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
1.0ms
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))

series4.5s

Counts
4 → 12
Calls
4 calls:
438.0ms
(cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))
50.0ms
(* (* t x) (* y 18.0))
797.0ms
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
3.2s
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))

simplify4.2s

Counts
69 → 69
Iterations
IterNodes
done5002
34578
21008
1314
0144

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize324.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))
2.0b
(* (* t x) (* y 18.0))
2.6b
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
62.0b
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-cbrt-cube add-exp-log
8×pow-prod-down prod-exp cbrt-unprod
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt log1p-expm1-u add-log-exp
2×fma-udef
1×cbrt-prod pow1/3 associate-*r* associate-*l* pow3 *-commutative rem-cbrt-cube
Counts
4 → 56
Calls
4 calls:
25.0ms
(cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))
32.0ms
(* (* t x) (* y 18.0))
1.0ms
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
1.0ms
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))))

series4.4s

Counts
4 → 12
Calls
4 calls:
418.0ms
(cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))
53.0ms
(* (* t x) (* y 18.0))
741.0ms
(fma z (* (* t x) (* y 18.0)) (- (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))))))
3.2s
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))))

simplify4.0s

Counts
68 → 68
Iterations
IterNodes
done5000
34771
21036
1328
0147

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes3.8s

Accuracy

70.4% (1.6b remaining)

Error of 1.6b against oracle of 0.0b and baseline of 5.3b

bsearch9.0ms

simplify52.0ms

Iterations
IterNodes
done91
291
187
060

end0.0ms

sample5.8s

Algorithm
intervals
Results
4.3s16446×body80valid