Details

Time bar (total: 39.4s)

sample73.0ms

Algorithm
intervals
Results
23.0ms275×body80valid
7.0ms95×body80nan

simplify319.0ms

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize49.0ms

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)))

rewrite142.0ms

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×sqrt-div insert-posit16
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 diff-log associate-*l* *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
20.0ms
(- (* z z) (* t a))
45.0ms
(* (* x y) z)
56.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* z z) (* t a))
40.0ms
(* (* x y) z)
233.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
126.0ms
(sqrt (- (* z z) (* t a)))

simplify3.2s

Counts
92 → 92
Iterations
IterNodes
done5000
21462
1364
0138

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
3.9b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite138.0ms

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×sqrt-div insert-posit16 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 diff-log associate-/r/
Counts
4 → 136
Calls
4 calls:
47.0ms
(/ (sqrt (- (* z z) (* t a))) z)
20.0ms
(- (* z z) (* t a))
27.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.0ms
(sqrt (- (* z z) (* t a)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (sqrt (- (* z z) (* t a))) z)
78.0ms
(- (* z z) (* t a))
194.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
106.0ms
(sqrt (- (* z z) (* t a)))

simplify3.3s

Counts
148 → 148
Iterations
IterNodes
done5000
21897
1560
0214

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
1.7b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.4b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×*-un-lft-identity add-cube-cbrt
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-cbrt-cube add-exp-log
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16 unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*r/ *-commutative
Counts
4 → 231
Calls
4 calls:
14.0ms
(- (* z z) (* t a))
23.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
107.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.0ms
(sqrt (- (* z z) (* t a)))

series638.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* z z) (* t a))
191.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
262.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
115.0ms
(sqrt (- (* z z) (* t a)))

simplify5.1s

Counts
243 → 243
Iterations
IterNodes
done5000
22848
1931
0334

prune3.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize84.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
7.7b
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite410.0ms

Algorithm
rewrite-expression-head
Rules
445×times-frac
307×add-sqr-sqrt
249×sqrt-prod
222×*-un-lft-identity add-cube-cbrt
98×associate-*r*
33×associate-*l*
31×associate-/r*
30×add-cbrt-cube add-exp-log
20×unswap-sqr
12×cbrt-undiv div-exp
10×div-inv
8×pow1 sqrt-div
6×prod-exp cbrt-unprod
4×associate-/r/ insert-posit16 add-log-exp
3×flip3-- flip-- associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 351
Calls
4 calls:
31.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
251.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
25.0ms
(sqrt (- (* z z) (* t a)))
23.0ms
(sqrt (- (* z z) (* t a)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
222.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
109.0ms
(sqrt (- (* z z) (* t a)))
113.0ms
(sqrt (- (* z z) (* t a)))

simplify7.6s

Counts
363 → 363
Iterations
IterNodes
done5000
24853
11473
0452

prune4.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

regimes2.8s

Accuracy

77.1% (4.5b remaining)

Error of 8.0b against oracle of 3.5b and baseline of 23.2b

bsearch143.0ms

Steps
ItersRangePoint
8
2.4182442546267315e+58
2.530003709242839e+61
7.410290891207557e+58
9
-1.4797030189529656e+112
-1.6711358187060892e+105
-1.6969835156997758e+105

simplify15.0ms

Iterations
IterNodes
done33
233
131
023

end0.0ms

sample1.9s

Algorithm
intervals
Results
971.0ms8817×body80valid
188.0ms2853×body80nan