Details

Time bar (total: 16.4s)

sample55.0ms

Algorithm
intervals
Results
25.0ms282×body80valid
7.0ms94×body80nan

simplify107.0ms

Counts
1 → 1
Iterations
IterNodes
done106
6106
597
477
358
237
122
012

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.5b
(* (* x y) z)
7.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite137.0ms

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:
18.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) z)
58.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0ms
(sqrt (- (* z z) (* t a)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* z z) (* t a))
35.0ms
(* (* x y) z)
117.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
done5001
21508
1385
0150

prune646.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.2b
(- (* z z) (* t a))
2.5b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
25×associate-/r*
18×add-cbrt-cube add-exp-log
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u div-inv
3×flip3-- flip--
2×clear-num frac-2neg prod-exp cbrt-unprod associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 146
Calls
4 calls:
21.0ms
(/ (sqrt (- (* z z) (* t a))) z)
18.0ms
(- (* z z) (* t a))
29.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (sqrt (- (* z z) (* t a))) z)
59.0ms
(- (* z z) (* t a))
110.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
86.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
158 → 158
Iterations
IterNodes
done5013
21959
1588
0226

prune923.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
2.5b
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
24.8b
(sqrt (- (* z z) (* t a)))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
54×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
27×add-cbrt-cube add-exp-log
22×*-un-lft-identity add-cube-cbrt
18×pow1/2
15×swap-sqr
13×times-frac
10×cbrt-undiv div-exp
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-- flip--
7×associate-/r*
6×prod-exp cbrt-unprod
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod associate-/r/ *-commutative associate-/l*
Counts
4 → 163
Calls
4 calls:
81.0ms
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
29.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
12.0ms
(sqrt (- (* z z) (* t a)))
32.0ms
(sqrt (- (* z z) (* t a)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
137.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
104.0ms
(sqrt (- (* z z) (* t a)))
96.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
175 → 175
Iterations
IterNodes
done5028
21887
1533
0217

prune908.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.7b
(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
2.6b
(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
115×add-sqr-sqrt
114×*-un-lft-identity add-cube-cbrt
60×add-exp-log
57×sqrt-prod
34×add-cbrt-cube div-exp
27×associate-/r*
25×associate-/l*
17×cbrt-undiv
12×div-inv
8×prod-exp
6×pow1 add-log-exp
5×rec-exp 1-exp
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u
2×clear-num frac-2neg flip3-- sqrt-div flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/ pow-flip inv-pow associate-/l/
Counts
4 → 245
Calls
4 calls:
19.0ms
(- (* z z) (* t a))
62.0ms
(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
44.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
17.0ms
(sqrt (- (* z z) (* t a)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
152.0ms
(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
189.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
116.0ms
(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts
257 → 257
Iterations
IterNodes
done5000
23072
1999
0375

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

regimes991.0ms

Accuracy

84.5% (3.0b remaining)

Error of 6.4b against oracle of 3.5b and baseline of 22.5b

bsearch135.0ms

Steps
ItersRangePoint
9
6.876815347956334e+134
1.292919298649766e+143
3.471068194478418e+142
9
-9.351864464929311e+91
-3.3514666867395575e+86
-3.962990925915687e+91

simplify10.0ms

Iterations
IterNodes
done35
235
132
023

end0.0ms

sample1.6s

Algorithm
intervals
Results
819.0ms8811×body80valid
328.0ms3007×body80nan