Details

Time bar (total: 17.6s)

sample68.0ms

Algorithm
intervals
Results
32.0ms284×body80valid
6.0ms96×body80nan

simplify108.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.9b
(* (* x y) z)
8.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
41.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
11.0ms
(sqrt (- (* z z) (* t a)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
39.0ms
(* (* x y) z)
133.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
88.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
88 → 88
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01341237
13411135
21495975
done5001974

prune374.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
2.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
16.0ms
(/ z (sqrt (- (* z z) (* t a))))
13.0ms
(- (* z z) (* t a))
53.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ z (sqrt (- (* z z) (* t a))))
39.0ms
(- (* z z) (* t a))
118.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
108.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
124 → 124
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01662031
14181847
215211643
done50001642

prune418.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.4b
(- (* z z) (* t a))
2.8b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
32×add-sqr-sqrt
30×add-cbrt-cube
27×prod-exp
25×associate-*r*
22×times-frac
21×*-un-lft-identity
19×pow1 add-cube-cbrt
15×cbrt-unprod
14×sqrt-prod
9×pow-prod-down
6×div-exp add-log-exp
5×unswap-sqr
4×sqrt-div associate-*r/ associate-*l*
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×associate-/r/ un-div-inv *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 108
Calls
4 calls:
47.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
8.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
17.0ms
(sqrt (- (* z z) (* t a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
39.0ms
(- (* z z) (* t a))
101.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
99.0ms
(sqrt (- (* z z) (* t a)))

simplify4.4s

Counts
120 → 120
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
01791998
14411678
212901360
349281359
done50001359

prune449.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize31.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
6.2b
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
23.8b
(cbrt (- (* z z) (* t a)))
23.8b
(cbrt (- (* z z) (* t a)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
189×times-frac
147×add-sqr-sqrt
102×add-cube-cbrt *-un-lft-identity
44×associate-*l*
33×associate-*r*
30×add-exp-log add-cbrt-cube
24×sqrt-prod
18×cbrt-prod
13×associate-/r*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×pow1 cbrt-div prod-exp cbrt-unprod
4×associate-/r/ add-log-exp
3×flip3-- flip-- associate-/l*
2×pow1/3 sqrt-div
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 209
Calls
4 calls:
9.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
122.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
12.0ms
(cbrt (- (* z z) (* t a)))
12.0ms
(cbrt (- (* z z) (* t a)))

series854.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
494.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
129.0ms
(cbrt (- (* z z) (* t a)))
144.0ms
(cbrt (- (* z z) (* t a)))

simplify2.5s

Counts
221 → 221
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03786093
110425874
236605367
done50015357

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.4b

regimes431.0ms

Accuracy

86.2% (2.7b remaining)

Error of 5.9b against oracle of 3.2b and baseline of 22.6b

bsearch183.0ms

Steps
ItersRangePoint
9
9.93242817157347e+75
3.0448476937474046e+84
2.112792157625963e+83
10
-9.541070983060701e+111
-6.828632073403998e+96
-1.6002570584328043e+108

simplify16.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
03264
14062
24161
35261
done5261

end0.0ms

sample1.7s

Algorithm
intervals
Results
778.0ms8851×body80valid
211.0ms2869×body80nan