Details

Time bar (total: 14.0s)

sample78.0ms

Algorithm
intervals
Results
25.0ms287×body80valid
15.0ms86×body80nan

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
9.5b
(/ (* (* 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)
42.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) z)
120.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
98.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune582.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.4b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite111.0ms

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:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
10.0ms
(- (* z z) (* t a))
73.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ z (sqrt (- (* z z) (* t a))))
42.0ms
(- (* z z) (* t a))
124.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
88.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
124 → 124
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01662031
14751855
229401657
done50011653

prune659.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.4b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite163.0ms

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:
14.0ms
(- (* z z) (* t a))
48.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
16.0ms
(sqrt (- (* z z) (* t a)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
98.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
152.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
112.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
104 → 104
Iterations

Useful iterations: 2 (380.0ms)

IterNodesCost
01611572
14371461
218871253
done50001253

prune488.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.6b
(- (* z z) (* t a))
3.4b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite161.0ms

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:
60.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
12.0ms
(- (* z z) (* t a))
75.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
51.0ms
(- (* z z) (* t a))
110.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
120 → 120
Iterations

Useful iterations: 2 (454.0ms)

IterNodesCost
01791998
15201787
223671380
done50001380

prune559.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.3b

regimes1.1s

Accuracy

85% (2.8b remaining)

Error of 6.4b against oracle of 3.6b and baseline of 22.3b

bsearch144.0ms

Steps
ItersRangePoint
9
1.3024678837784223e+151
3.1155849420069337e+159
2.4679280727529663e+151
10
-3.614756268483021e+161
-1.626953607814572e+151
-2.6962331905453547e+153

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12729
23029
done3029

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8822×body80valid
215.0ms3000×body80nan