Details

Time bar (total: 18.2s)

sample63.0ms

Algorithm
intervals
Results
29.0ms491×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (95.0ms)

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: 6.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
0.0b
(- (* z z) t)
6.4b
(* (* y 4.0) (- (* z z) t))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
16×prod-diff
11×add-sqr-sqrt
10×distribute-rgt-in distribute-lft-in associate--r+
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×sub-neg
4×associate-*r*
3×expm1-log1p-u flip3-- pow-prod-down prod-exp flip-- cbrt-unprod log1p-expm1-u
2×fma-neg diff-log associate-*r/ difference-of-squares
1×associate-*l* *-commutative
Counts
3 → 78
Calls
3 calls:
14.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
13.0ms
(- (* z z) t)
46.0ms
(* (* y 4.0) (- (* z z) t))

series176.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
23.0ms
(- (* z z) t)
70.0ms
(* (* y 4.0) (- (* z z) t))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01481288
13901137
21271994
done5001966

prune254.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) (* (* y 4.0) (fma z z (- t))))
6.4b
(* (* y 4.0) (fma z z (- t)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×fma-udef add-log-exp
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u associate--r+
1×sub-neg flip3-- fma-neg diff-log associate-*l* prod-diff *-commutative flip--
Counts
2 → 40
Calls
2 calls:
15.0ms
(- (* x x) (* (* y 4.0) (fma z z (- t))))
19.0ms
(* (* y 4.0) (fma z z (- t)))

series192.0ms

Counts
2 → 6
Calls
2 calls:
103.0ms
(- (* x x) (* (* y 4.0) (fma z z (- t))))
89.0ms
(* (* y 4.0) (fma z z (- t)))

simplify3.8s

Counts
46 → 46
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
091713
1240671
2911585
34557562
done5000562

prune196.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
6.4b
(sqrt (- (* z z) t))
6.4b
(sqrt (- (* z z) t))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
18×add-exp-log sqrt-div add-cbrt-cube
16×add-sqr-sqrt sqrt-prod
14×associate-*r*
10×add-cube-cbrt *-un-lft-identity associate-*r/
9×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*l/ *-commutative
Counts
4 → 97
Calls
4 calls:
60.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
143.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
19.0ms
(sqrt (- (* z z) t))
14.0ms
(sqrt (- (* z z) t))

series327.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
99.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
68.0ms
(sqrt (- (* z z) t))
56.0ms
(sqrt (- (* z z) t))

simplify1.9s

Counts
109 → 109
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01421771
13851408
213431175
done50001169

prune379.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
6.4b
(sqrt (- (* z z) t))
6.4b
(sqrt (- (* z z) t))
6.4b
(sqrt (- (* z z) t))

rewrite607.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-- flip--
28×frac-times
26×associate-*r/
23×sqrt-prod
21×pow1
18×add-exp-log add-cbrt-cube
17×add-sqr-sqrt
14×associate-*l/
10×add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 113
Calls
4 calls:
544.0ms
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
22.0ms
(sqrt (- (* z z) t))
14.0ms
(sqrt (- (* z z) t))
16.0ms
(sqrt (- (* z z) t))

series288.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
63.0ms
(sqrt (- (* z z) t))
58.0ms
(sqrt (- (* z z) t))
75.0ms
(sqrt (- (* z z) t))

simplify1.7s

Counts
125 → 125
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01883314
15142677
217811889
done50001804

prune655.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.4b

regimes393.0ms

Accuracy

86.6% (0.4b remaining)

Error of 3.2b against oracle of 2.8b and baseline of 6.1b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02136
12636
done2636

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s15832×body80valid