Details

Time bar (total: 28.5s)

sample88.0ms

Algorithm
intervals
Results
46.0ms285×body80valid
14.0ms97×body80nan

simplify137.0ms

Counts
1 → 1
Iterations
IterNodes
done103
6103
597
470
353
236
121
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
6.2b
(* (* x y) z)
9.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.0b
(sqrt (- (* z z) (* t a)))

rewrite427.0ms

Algorithm
rewrite-expression-head
Rules
940×add-sqr-sqrt
440×times-frac
430×associate-*l*
408×sqrt-prod
360×*-un-lft-identity
263×unswap-sqr
250×difference-of-squares
160×add-cube-cbrt
132×associate-*r*
100×distribute-lft-out--
94×*-commutative
50×swap-sqr
22×associate-/l*
20×associate-/r*
18×add-cbrt-cube add-exp-log
10×pow1
6×prod-exp cbrt-unprod add-log-exp
4×sqrt-div insert-posit16
3×cbrt-undiv flip3-- div-exp pow-prod-down flip--
2×associate-/r/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 590
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) z)
164.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
94.0ms
(sqrt (- (* z z) (* t a)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* z z) (* t a))
43.0ms
(* (* x y) z)
125.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
122.0ms
(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts
602 → 602
Iterations
IterNodes
done5012
23519
11358
0599

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.0b
(sqrt (- (* z z) (* t a)))

rewrite673.0ms

Algorithm
rewrite-expression-head
Rules
339×add-sqr-sqrt
155×sqrt-prod
148×*-un-lft-identity
124×times-frac
100×difference-of-squares
80×unswap-sqr
69×associate-*r*
67×add-cube-cbrt
55×associate-*l*
40×associate-/r* distribute-lft-out--
26×associate-*r/
22×*-commutative
20×swap-sqr
18×add-cbrt-cube add-exp-log
10×pow1
7×associate-/l*
6×sqrt-div prod-exp cbrt-unprod add-log-exp
4×flip3-- associate-/r/ insert-posit16 flip--
3×cbrt-undiv clear-num div-exp pow-prod-down
2×frac-2neg un-div-inv div-inv
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 286
Calls
4 calls:
98.0ms
(/ z (sqrt (- (* z z) (* t a))))
81.0ms
(- (* z z) (* t a))
418.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
54.0ms
(sqrt (- (* z z) (* t a)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ z (sqrt (- (* z z) (* t a))))
51.0ms
(- (* z z) (* t a))
126.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
140.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
298 → 298
Iterations
IterNodes
done5000
22381
1803
0295

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.2b
(- (* z z) (* t a))
3.3b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
24.0b
(sqrt (- (* z z) (* t a)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
392×add-sqr-sqrt
214×associate-*r*
161×*-un-lft-identity sqrt-prod
136×times-frac
109×unswap-sqr
100×difference-of-squares
81×associate-*r/
71×add-cube-cbrt
61×associate-*l*
48×add-exp-log
40×associate-/r* distribute-lft-out--
30×add-cbrt-cube
27×prod-exp
24×*-commutative
20×swap-sqr
19×pow1
15×cbrt-unprod
9×pow-prod-down
8×associate-/l*
6×sqrt-div div-exp un-div-inv add-log-exp
4×clear-num flip3-- associate-/r/ insert-posit16 flip--
3×cbrt-undiv rec-exp 1-exp
2×frac-2neg div-inv
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 337
Calls
4 calls:
305.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
43.0ms
(- (* z z) (* t a))
1.0s
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
69.0ms
(sqrt (- (* z z) (* t a)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
72.0ms
(- (* z z) (* t a))
118.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify2.7s

Counts
349 → 349
Iterations
IterNodes
done5002
23415
11007
0328

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.2b
(- (* z z) (* t a))
3.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.0b
(sqrt (- (* z z) (* t a)))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
1864×add-sqr-sqrt
1608×times-frac
951×*-un-lft-identity
765×sqrt-prod
583×add-cube-cbrt
460×difference-of-squares
387×unswap-sqr
379×associate-*l*
195×associate-*r*
184×distribute-lft-out--
157×*-commutative
92×swap-sqr
70×associate-/r*
52×associate-/l*
28×associate-/r/
18×add-cbrt-cube add-exp-log
15×div-inv
7×cbrt-undiv div-exp
6×sqrt-div add-log-exp
5×pow1
4×flip3-- insert-posit16 flip-- associate-/l/
3×clear-num frac-2neg
2×prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 1046
Calls
4 calls:
115.0ms
(/ (sqrt (- (* z z) (* t a))) z)
48.0ms
(- (* z z) (* t a))
181.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
100.0ms
(sqrt (- (* z z) (* t a)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (sqrt (- (* z z) (* t a))) z)
69.0ms
(- (* z z) (* t a))
155.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
85.0ms
(sqrt (- (* z z) (* t a)))

simplify3.2s

Counts
1058 → 1058
Iterations
IterNodes
done5000
13250
01033

prune4.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.3b

regimes1.2s

Accuracy

83.1% (3.2b remaining)

Error of 6.3b against oracle of 3.1b and baseline of 22.1b

bsearch155.0ms

Steps
ItersRangePoint
6
2.2894762542141246e+79
1.0557140695987437e+80
2.574280554580049e+79
6
-1.6290502733481186e+78
-1.7079472454689577e+77
-1.510233764806379e+78

simplify5.0ms

Iterations
IterNodes
done35
135
027

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s8828×body80valid
381.0ms3015×body80nan