Details

Time bar (total: 16.8s)

sample80.0ms

Algorithm
intervals
Results
27.0ms291×body80valid
7.0ms96×body80nan

simplify100.0ms

Counts
1 → 1
Iterations
IterNodes
done118
5118
497
372
246
122
012

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma z z (- (* a t)))
1.6b
(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
9.5b
(/ (* z y) (sqrt (fma z z (- (* a t)))))
23.1b
(sqrt (fma z z (- (* a t))))

rewrite31.0ms

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 sqrt-prod
10×associate-*l*
7×pow1
6×associate-/r*
5×prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×associate-*r*
2×div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative fma-udef associate-/l* unswap-sqr
Counts
4 → 86
Calls
4 calls:
0.0ms
(fma z z (- (* a t)))
19.0ms
(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
8.0ms
(/ (* z y) (sqrt (fma z z (- (* a t)))))
1.0ms
(sqrt (fma z z (- (* a t))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma z z (- (* a t)))
148.0ms
(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
82.0ms
(/ (* z y) (sqrt (fma z z (- (* a t)))))
119.0ms
(sqrt (fma z z (- (* a t))))

simplify1.1s

Counts
98 → 98
Iterations
IterNodes
done5000
21731
1312
0130

prune844.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize55.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t)))))) x)
5.0b
(/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t))))))
23.1b
(sqrt (fma z z (- (* a t))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
27×add-cbrt-cube add-exp-log
21×add-sqr-sqrt
18×times-frac
17×*-un-lft-identity add-cube-cbrt
13×associate-*l*
9×associate-/r*
8×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r*
2×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div associate-*l/ div-inv
1×clear-num frac-2neg flip3-- pow-prod-down *-commutative flip-- associate-/l* unswap-sqr associate-/l/
Counts
4 → 107
Calls
4 calls:
132.0ms
(* (/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t)))))) x)
52.0ms
(/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t))))))
2.0ms
(sqrt (fma z z (- (* a t))))
19.0ms
(sqrt (- (* z z) (* t a)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t)))))) x)
184.0ms
(/ (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (sqrt (sqrt (fma z z (- (* a t))))))
114.0ms
(sqrt (fma z z (- (* a t))))
83.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
119 → 119
Iterations
IterNodes
done5002
22671
1518
0194

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize79.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y)
6.4b
(* (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
23.1b
(sqrt (- (* z z) (* t a)))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
58×add-sqr-sqrt
57×times-frac
45×*-un-lft-identity add-cube-cbrt
36×associate-*r*
34×associate-*l*
30×add-cbrt-cube add-exp-log
13×pow1
12×sqrt-div prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×expm1-log1p-u flip3-- pow-prod-down associate-*l/ associate-/r/ log1p-expm1-u flip-- add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
1×frac-times associate-*r/
Counts
4 → 151
Calls
4 calls:
49.0ms
(* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y)
102.0ms
(* (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y)
181.0ms
(* (* (/ z (sqrt (sqrt (- (* z z) (* t a))))) y) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
88.0ms
(sqrt (- (* z z) (* t a)))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts
163 → 163
Iterations
IterNodes
done5002
24416
1672
0240

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize139.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (- (* z z) (* t a)))
23.1b
(sqrt (- (* z z) (* t a)))
23.1b
(sqrt (- (* z z) (* t a)))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite57.0ms

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 log1p-expm1-u flip-- add-log-exp
Counts
4 → 68
Calls
4 calls:
10.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))
16.0ms
(sqrt (- (* z z) (* t a)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* z z) (* t a)))
114.0ms
(sqrt (- (* z z) (* t a)))
98.0ms
(sqrt (- (* z z) (* t a)))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
80 → 80
Iterations
IterNodes
done5000
32952
2530
1140
052

prune912.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.4b

regimes1.2s

Accuracy

82.1% (3.6b remaining)

Error of 7.2b against oracle of 3.5b and baseline of 23.7b

bsearch65.0ms

Steps
ItersRangePoint
0
7.590712924645989e+117
7.695838515569772e+117
7.64327572010788e+117
7
-6.499354134947939e+42
-2.420896724821489e+41
-6.395336884503867e+42

simplify7.0ms

Iterations
IterNodes
done37
237
134
026

end0.0ms

sample1.9s

Algorithm
intervals
Results
884.0ms8830×body80valid
204.0ms2961×body80nan