Details

Time bar (total: 21.5s)

sample64.0ms

Algorithm
intervals
Results
30.0ms497×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (115.0ms)

IterNodesCost
01113
12113
25213
317113
434612
558612
669812
780512
8104212
9122512
10122812
done122812

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- t (* z z))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef difference-of-squares
Counts
2 → 31
Calls
2 calls:
6.0ms
(- t (* z z))
0.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

series186.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(- t (* z z))
126.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

simplify2.2s

Counts
37 → 37
Iterations

Useful iterations: 4 (977.0ms)

IterNodesCost
065421
1139415
2341357
3898348
42934329
done5001329

prune121.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b
(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
5.3b
(cbrt (- t (* z z)))
5.3b
(cbrt (- t (* z z)))
5.3b
(cbrt (- t (* z z)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- difference-of-squares
1×fma-udef
Counts
4 → 58
Calls
4 calls:
0.0ms
(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
3.0ms
(cbrt (- t (* z z)))
4.0ms
(cbrt (- t (* z z)))
6.0ms
(cbrt (- t (* z z)))

series1.3s

Counts
4 → 12
Calls
4 calls:
176.0ms
(fma (* y 4.0) (* (* (cbrt (- t (* z z))) (cbrt (- t (* z z)))) (cbrt (- t (* z z)))) (* x x))
464.0ms
(cbrt (- t (* z z)))
387.0ms
(cbrt (- t (* z z)))
319.0ms
(cbrt (- t (* z z)))

simplify3.4s

Counts
70 → 70
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
0971117
12141087
2518834
31292767
44201743
done5000743

prune450.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b
(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
2.0ms
(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
1.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
1.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
1.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

series1.2s

Counts
4 → 12
Calls
4 calls:
677.0ms
(cbrt (fma (* y 4.0) (- t (* z z)) (* x x)))
167.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
202.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
156.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

simplify2.8s

Counts
55 → 55
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
070924
1142920
2361799
3977781
43588775
done5000775

prune380.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

localize60.0ms

Local error

Found 4 expressions with local error:

4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))
4.8b
(fma (* y 4.0) (- t (* z z)) (* x x))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
0.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
0.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
0.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
0.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

series683.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
219.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
144.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))
160.0ms
(fma (* y 4.0) (- t (* z z)) (* x x))

simplify1.8s

Counts
52 → 52
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
029832
156832
2154708
3439692
41797692
done5001692

prune365.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 3.9b

regimes429.0ms

Accuracy

91.7% (0.1b remaining)

Error of 5.1b against oracle of 5.1b and baseline of 6.0b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01526
11726
done1726

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.7s15680×body80valid