Details

Time bar (total: 17.6s)

sample62.0ms

Algorithm
intervals
Results
26.0ms275×body80valid
8.0ms95×body80nan

simplify145.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.7b
(* (* x y) z)
8.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite96.0ms

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))
18.0ms
(* (* x y) z)
45.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0ms
(sqrt (- (* z z) (* t a)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) z)
103.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
79.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
done5001
21508
1385
0150

prune608.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize50.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.6b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×*-un-lft-identity add-cube-cbrt
33×associate-*r*
30×add-cbrt-cube add-exp-log
16×sqrt-div
15×associate-*l*
9×cbrt-undiv associate-/r* div-exp prod-exp cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 153
Calls
4 calls:
30.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
115.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
29.0ms
(sqrt (- (* z z) (* t a)))
22.0ms
(sqrt (- (* z z) (* t a)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
102.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
94.0ms
(sqrt (- (* z z) (* t a)))
80.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
165 → 165
Iterations
IterNodes
done5003
22417
1675
0233

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.8b

localize61.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a))))))
5.6b
(* (* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
66×associate-*r*
60×sqrt-prod
57×add-cbrt-cube
54×times-frac prod-exp
46×add-sqr-sqrt
44×*-un-lft-identity add-cube-cbrt
28×cbrt-unprod
21×div-exp
20×pow1
12×sqrt-div
11×cbrt-undiv
9×pow-prod-down
6×rec-exp 1-exp
4×expm1-log1p-u flip3-- associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u flip-- add-log-exp
3×un-div-inv
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*l/ *-commutative div-inv
Counts
4 → 178
Calls
4 calls:
57.0ms
(* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a))))))
168.0ms
(* (* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms
(sqrt (- (* z z) (* t a)))
14.0ms
(sqrt (- (* z z) (* t a)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a))))))
116.0ms
(* (* (* x y) (/ 1 (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
98.0ms
(sqrt (- (* z z) (* t a)))
111.0ms
(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts
190 → 190
Iterations
IterNodes
done5001
22683
1840
0277

prune949.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.8b

localize60.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
Counts
4 → 72
Calls
4 calls:
23.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (- (* z z) (* t a)))
105.0ms
(sqrt (- (* z z) (* t a)))
111.0ms
(sqrt (- (* z z) (* t a)))
69.0ms
(sqrt (- (* z z) (* t a)))

simplify2.6s

Counts
84 → 84
Iterations
IterNodes
done5000
44036
31240
2398
1133
053

prune571.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 2.8b

regimes1.1s

Accuracy

80.8% (3.9b remaining)

Error of 7.4b against oracle of 3.4b and baseline of 23.8b

bsearch138.0ms

Steps
ItersRangePoint
9
5.011112315551321e+98
1.162298132228303e+106
3.3038276235904442e+103
8
-1.381541080692419e+19
-11403404315933134.0
-1.3631090406228963e+19

simplify8.0ms

Iterations
IterNodes
done30
230
128
022

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8817×body80valid
191.0ms2853×body80nan