Details

Time bar (total: 16.2s)

sample63.0ms

Algorithm
intervals
Results
24.0ms283×body80valid
6.0ms81×body80nan

simplify77.0ms

Counts
1 → 1
Iterations
IterNodes
done114
5114
493
368
245
121
012

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* a t))
1.3b
(/ (* x y) (sqrt (- (* z z) (* a t))))
8.9b
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
23.2b
(sqrt (- (* z z) (* a t)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac associate-*l* sqrt-prod
7×pow1
6×associate-/r* sqrt-div add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv flip3-- div-exp associate-/r/ flip--
3×associate-*r*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*l/ *-commutative associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
11.0ms
(- (* z z) (* a t))
28.0ms
(/ (* x y) (sqrt (- (* z z) (* a t))))
53.0ms
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
10.0ms
(sqrt (- (* z z) (* a t)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* z z) (* a t))
126.0ms
(/ (* x y) (sqrt (- (* z z) (* a t))))
133.0ms
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
109.0ms
(sqrt (- (* z z) (* a t)))

simplify1.4s

Counts
100 → 100
Iterations
IterNodes
done5000
22100
1392
0144

prune828.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* a t))))
0.8b
(- (* z z) (* a t))
2.8b
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
23.2b
(sqrt (- (* z z) (* a t)))

rewrite109.0ms

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×flip3-- associate-/r/ 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 diff-log associate-*l* associate-*r/ *-commutative
Counts
4 → 112
Calls
4 calls:
20.0ms
(/ z (sqrt (- (* z z) (* a t))))
6.0ms
(- (* z z) (* a t))
63.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
14.0ms
(sqrt (- (* z z) (* a t)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ z (sqrt (- (* z z) (* a t))))
56.0ms
(- (* z z) (* a t))
163.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
98.0ms
(sqrt (- (* z z) (* a t)))

simplify2.0s

Counts
124 → 124
Iterations
IterNodes
done5001
22991
1475
0166

prune983.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* y x) (sqrt (sqrt (- (* z z) (* a t)))))
8.9b
(* (/ (/ (* y x) (sqrt (sqrt (- (* z z) (* a t))))) (sqrt (sqrt (- (* z z) (* a t))))) z)
23.2b
(sqrt (- (* z z) (* a t)))
23.2b
(sqrt (- (* z z) (* a t)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
243×sqrt-prod
228×times-frac
141×associate-*l*
108×add-sqr-sqrt
95×*-un-lft-identity add-cube-cbrt
48×sqrt-div
23×add-cbrt-cube add-exp-log
22×associate-/r/
13×flip3-- flip--
11×div-inv
9×associate-/r*
8×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×add-log-exp unswap-sqr
3×associate-*r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative associate-/l*
Counts
4 → 231
Calls
4 calls:
31.0ms
(/ (* y x) (sqrt (sqrt (- (* z z) (* a t)))))
171.0ms
(* (/ (/ (* y x) (sqrt (sqrt (- (* z z) (* a t))))) (sqrt (sqrt (- (* z z) (* a t))))) z)
8.0ms
(sqrt (- (* z z) (* a t)))
7.0ms
(sqrt (- (* z z) (* a t)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (* y x) (sqrt (sqrt (- (* z z) (* a t)))))
141.0ms
(* (/ (/ (* y x) (sqrt (sqrt (- (* z z) (* a t))))) (sqrt (sqrt (- (* z z) (* a t))))) z)
134.0ms
(sqrt (- (* z z) (* a t)))
92.0ms
(sqrt (- (* z z) (* a t)))

simplify1.8s

Counts
243 → 243
Iterations
IterNodes
done5001
23466
1719
0279

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* a t))
2.5b
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
9.0b
(/ (* y z) (sqrt (- (* z z) (* a t))))
23.2b
(sqrt (- (* z z) (* a t)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac associate-*r* sqrt-prod
7×pow1
6×associate-/r* sqrt-div add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv flip3-- div-exp associate-/r/ flip--
3×associate-*l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*r/ *-commutative associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
7.0ms
(- (* z z) (* a t))
45.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
31.0ms
(/ (* y z) (sqrt (- (* z z) (* a t))))
7.0ms
(sqrt (- (* z z) (* a t)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* a t))
120.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
96.0ms
(/ (* y z) (sqrt (- (* z z) (* a t))))
130.0ms
(sqrt (- (* z z) (* a t)))

simplify942.0ms

Counts
100 → 100
Iterations
IterNodes
done5001
22008
1395
0143

prune854.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes1.0s

Accuracy

84.5% (3.1b remaining)

Error of 6.5b against oracle of 3.4b and baseline of 23.6b

bsearch162.0ms

Steps
ItersRangePoint
7
4.962524782877993e+148
5.8027159941114316e+150
6.533659553749963e+149
5
3.2197111124467914e-171
1.1308082089162385e-170
5.226961588256763e-171
6
-6.068809377993764e+74
-8.792947008942685e+73
-4.360527887622533e+74

simplify11.0ms

Iterations
IterNodes
done67
467
363
250
145
036

end0.0ms

sample1.5s

Algorithm
intervals
Results
729.0ms8857×body80valid
273.0ms2816×body80nan