Details

Time bar (total: 16.4s)

sample46.0ms

Algorithm
intervals
Results
24.0ms286×body80valid
7.0ms95×body80nan

simplify138.0ms

Counts
1 → 1
Iterations
IterNodes
done112
6112
5111
496
372
246
122
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
5.7b
(* (* x y) z)
6.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) z)
50.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) z)
98.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
102 → 102
Iterations
IterNodes
done5000
21679
1385
0150

prune540.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
24×associate-*r* sqrt-prod
18×add-cbrt-cube add-exp-log
10×pow1
6×associate-/r* sqrt-div prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff associate-*r/ *-commutative
Counts
4 → 126
Calls
4 calls:
23.0ms
(/ z (sqrt (- (* z z) (* t a))))
19.0ms
(- (* z z) (* t a))
65.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ z (sqrt (- (* z z) (* t a))))
48.0ms
(- (* z z) (* t a))
122.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
105.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
138 → 138
Iterations
IterNodes
done5000
21909
1501
0182

prune870.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
1.0b
(- (* z z) (* t a))
3.2b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
32×add-sqr-sqrt
30×add-cbrt-cube
27×prod-exp
25×associate-*r*
22×times-frac
21×*-un-lft-identity
19×pow1 add-cube-cbrt
15×cbrt-unprod
14×sqrt-prod
9×pow-prod-down
6×div-exp add-log-exp
5×unswap-sqr
4×expm1-log1p-u sqrt-div associate-*l* associate-*r/ insert-posit16 log1p-expm1-u
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×associate-/r/ un-div-inv *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 122
Calls
4 calls:
37.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
9.0ms
(- (* z z) (* t a))
54.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
10.0ms
(sqrt (- (* z z) (* t a)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
49.0ms
(- (* z z) (* t a))
112.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
109.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
134 → 134
Iterations
IterNodes
done5001
21748
1505
0195

prune735.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.2b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.0b
(* (/ z (sqrt (- (* z z) (* t a)))) y)
3.1b
(* x (* (/ z (sqrt (- (* z z) (* t a)))) y))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
27×associate-*l*
20×*-un-lft-identity times-frac add-cube-cbrt
18×add-cbrt-cube add-exp-log
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×add-log-exp
4×expm1-log1p-u sqrt-div associate-*r* pow-prod-down insert-posit16 log1p-expm1-u
3×flip3-- flip-- unswap-sqr
2×cbrt-undiv div-exp associate-*l/ associate-/r/ *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-*r/ div-inv
Counts
4 → 106
Calls
4 calls:
16.0ms
(- (* z z) (* t a))
61.0ms
(* (/ z (sqrt (- (* z z) (* t a)))) y)
80.0ms
(* x (* (/ z (sqrt (- (* z z) (* t a)))) y))
20.0ms
(sqrt (- (* z z) (* t a)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* z z) (* t a))
83.0ms
(* (/ z (sqrt (- (* z z) (* t a)))) y)
99.0ms
(* x (* (/ z (sqrt (- (* z z) (* t a)))) y))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
118 → 118
Iterations
IterNodes
done5002
21391
1410
0169

prune825.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.2b

regimes854.0ms

Accuracy

85.5% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 22.3b

bsearch164.0ms

Steps
ItersRangePoint
9
1.3811436676451923e+110
7.486911991823205e+115
1.1848486164183457e+114
7
-2.513744904282275e+156
-1.854306054422796e+154
-1.8913959868564195e+154

simplify6.0ms

Iterations
IterNodes
done33
233
130
022

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s8876×body80valid
815.0ms2933×body80nan