Details

Time bar (total: 9.4s)

sample35.0ms

Algorithm
intervals
Results
18.0ms491×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (56.0ms)

IterNodesCost
01113
12113
25113
314813
433412
558212
671612
780512
898612
9133212
10133512
done133512

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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:
3.0ms
(- (* z z) t)
9.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
15.0ms
(* (* y 4.0) (- (* z z) t))

series177.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(- (* z z) t)
86.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
67.0ms
(* (* y 4.0) (- (* z z) t))

simplify926.0ms

Counts
87 → 87
Iterations

Useful iterations: done (923.0ms)

IterNodesCost
01481288
13921137
21419999
done5001990

prune235.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×prod-diff
7×add-cube-cbrt *-un-lft-identity
6×associate-*l*
5×distribute-rgt-in distribute-lft-in
4×pow1 add-exp-log associate-*r* add-cbrt-cube add-log-exp
3×sub-neg
2×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u difference-of-squares
1×distribute-lft-neg-out distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in fma-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 56
Calls
2 calls:
3.0ms
(- (* z z) t)
18.0ms
(* (- (* y 4.0)) (- (* z z) t))

series93.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(- (* z z) t)
65.0ms
(* (- (* y 4.0)) (- (* z z) t))

simplify778.0ms

Counts
62 → 62
Iterations

Useful iterations: done (775.0ms)

IterNodesCost
0107835
1282735
21168644
done5000635

prune184.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.9b

localize12.0ms

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)))
5.2b
(sqrt (- (* z z) t))
5.2b
(sqrt (- (* z z) t))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×sqrt-div
17×sqrt-prod
14×associate-*r*
13×pow1
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
7×associate-*l*
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp difference-of-squares
3×distribute-lft-neg-out
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
1×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
Counts
4 → 100
Calls
4 calls:
15.0ms
(* (- (* y 4.0)) (sqrt (- (* z z) t)))
36.0ms
(* (* (- (* y 4.0)) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
6.0ms
(sqrt (- (* z z) t))
6.0ms
(sqrt (- (* z z) t))

series244.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (- (* y 4.0)) (sqrt (- (* z z) t)))
69.0ms
(* (* (- (* y 4.0)) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
54.0ms
(sqrt (- (* z z) t))
50.0ms
(sqrt (- (* z z) t))

simplify898.0ms

Counts
112 → 112
Iterations

Useful iterations: done (894.0ms)

IterNodesCost
01401821
13771485
215111290
done50001288

prune393.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* (- (* y 4.0)) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
5.2b
(sqrt (- (* z z) t))
5.2b
(sqrt (- (* z z) t))
5.2b
(sqrt (- (* z z) t))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-- flip--
28×frac-times
26×associate-*r/
23×sqrt-prod
17×add-sqr-sqrt
16×pow1
14×associate-*l/
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×distribute-lft-neg-out rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 111
Calls
4 calls:
119.0ms
(* (* (* (- (* y 4.0)) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
6.0ms
(sqrt (- (* z z) t))
6.0ms
(sqrt (- (* z z) t))
6.0ms
(sqrt (- (* z z) t))

series229.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* (* (- (* y 4.0)) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
55.0ms
(sqrt (- (* z z) t))
51.0ms
(sqrt (- (* z z) t))
57.0ms
(sqrt (- (* z z) t))

simplify962.0ms

Counts
123 → 123
Iterations

Useful iterations: done (957.0ms)

IterNodesCost
01783266
14942660
217761923
done50011920

prune486.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.9b

regimes245.0ms

Accuracy

83.9% (0.5b remaining)

Error of 3.3b against oracle of 2.8b and baseline of 6.1b

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02036
13336
24536
35436
done5436

end0.0ms

sample863.0ms

Algorithm
intervals
Results
479.0ms15938×body80valid