Details

Time bar (total: 13.1s)

sample38.0ms

Algorithm
intervals
Results
13.0ms276×body80valid
4.0ms88×body80nan

simplify79.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
6.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite85.0ms

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))
17.0ms
(* (* x y) z)
49.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
119.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
95.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
88 → 88
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune304.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite121.0ms

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:
18.0ms
(/ z (sqrt (- (* z z) (* t a))))
13.0ms
(- (* z z) (* t a))
74.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ z (sqrt (- (* z z) (* t a))))
59.0ms
(- (* z z) (* t a))
149.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
97.0ms
(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts
124 → 124
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01662031
14751855
229401657
done50011653

prune444.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* y (/ z (sqrt (- (* z z) (* t a)))))
0.8b
(- (* z z) (* t a))
1.8b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
8.0ms
(- (* z z) (* t a))
45.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.0ms
(sqrt (- (* z z) (* t a)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
46.0ms
(- (* z z) (* t a))
136.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
91.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
104 → 104
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
01611572
14371457
218911253
done50001253

prune344.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.8b

localize48.0ms

Local error

Found 4 expressions with local error:

2.9b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
22.3b
(sqrt (- (* z z) (* t a)))
22.3b
(sqrt (- (* z z) (* t a)))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
10.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))
17.0ms
(sqrt (- (* z z) (* t a)))
17.0ms
(sqrt (- (* z z) (* t a)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
90 → 90
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01491524
12841390
28211292
337271286
done50011278

prune459.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.8b

regimes513.0ms

Accuracy

85.9% (2.7b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 22.6b

bsearch143.0ms

Steps
ItersRangePoint
11
1.8434798023201203e+65
5.54089522496413e+95
4.020794709845026e+94
9
-3.903711985203957e+156
-5.880305990614135e+148
-2.4659981599653674e+149

simplify15.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02231
13329
24329
34529
done4529

end0.0ms

sample2.1s

Algorithm
intervals
Results
703.0ms8885×body80valid
205.0ms2899×body80nan