Details

Time bar (total: 15.2s)

sample58.0ms

Algorithm
intervals
Results
26.0ms286×body80valid
8.0ms95×body80nan

simplify109.0ms

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: 21.5b

localize36.0ms

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)))

rewrite70.0ms

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))
14.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
40.0ms
(* (* x y) z)
99.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
86.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
102 → 102
Iterations
IterNodes
done5001
21508
1385
0150

prune616.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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))))
16.0ms
(- (* z z) (* t a))
76.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms
(sqrt (- (* z z) (* t a)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
131.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
138 → 138
Iterations
IterNodes
done5000
21799
1501
0183

prune768.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize53.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))) y) x)
23.6b
(sqrt (- (* z z) (* t a)))
23.6b
(sqrt (- (* z z) (* t a)))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×add-cbrt-cube
16×pow1
15×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×associate-*l/
6×sqrt-div pow-prod-down
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r* flip--
1×frac-times associate-*l* associate-*r/ *-commutative
Counts
4 → 87
Calls
4 calls:
382.0ms
(* (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))) y) x)
13.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))

series613.0ms

Counts
4 → 12
Calls
4 calls:
321.0ms
(* (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))) y) x)
111.0ms
(sqrt (- (* z z) (* t a)))
109.0ms
(sqrt (- (* z z) (* t a)))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
99 → 99
Iterations
IterNodes
done5000
21328
1368
0141

prune888.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.0b
(* x (/ z (sqrt (- (* z z) (* t a)))))
2.6b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
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×associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div pow-prod-down insert-posit16 log1p-expm1-u
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 106
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
37.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
45.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* z z) (* t a))
74.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
130.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
118 → 118
Iterations
IterNodes
done5000
21446
1444
0178

prune617.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.2b

regimes866.0ms

Accuracy

87.6% (2.3b remaining)

Error of 5.4b against oracle of 3.1b and baseline of 21.8b

bsearch113.0ms

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

simplify8.0ms

Iterations
IterNodes
done35
235
133
025

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8876×body80valid
192.0ms2933×body80nan