Details

Time bar (total: 12.5s)

sample74.0ms

Algorithm
intervals
Results
26.0ms298×body80valid
9.0ms113×body80nan

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37314
49814
511914
done11914

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.5b
(* (* x y) z)
9.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite105.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
17.0ms
(- (* z z) (* t a))
38.0ms
(* (* x y) z)
34.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
123.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
90.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01461331
13861225
222651080
done50001077

prune453.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.7b
(* x (* z y))
9.4b
(/ (* x (* z y)) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite94.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*l* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
12.0ms
(- (* z z) (* t a))
25.0ms
(* x (* z y))
32.0ms
(/ (* x (* z y)) (sqrt (- (* z z) (* t a))))
22.0ms
(sqrt (- (* z z) (* t a)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* z z) (* t a))
47.0ms
(* x (* z y))
131.0ms
(/ (* x (* z y)) (sqrt (- (* z z) (* t a))))
94.0ms
(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts
98 → 98
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01431330
13781226
218451081
done50011076

prune463.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(* x (/ (* z y) (sqrt (- (* z z) (* t a)))))
8.7b
(/ (* z y) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac associate-*r* sqrt-prod
7×pow1
6×sqrt-div associate-/r* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u flip3-- div-exp associate-/r/ flip-- log1p-expm1-u
3×associate-*l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 98
Calls
4 calls:
20.0ms
(- (* z z) (* t a))
67.0ms
(* x (/ (* z y) (sqrt (- (* z z) (* t a)))))
22.0ms
(/ (* z y) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
97.0ms
(* x (/ (* z y) (sqrt (- (* z z) (* t a)))))
78.0ms
(/ (* z y) (sqrt (- (* z z) (* t a))))
111.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
110 → 110
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01551669
14221538
222461347
done50001346

prune447.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(* (/ (* z y) (sqrt (- (* z z) (* t a)))) x)
8.7b
(/ (* z y) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac associate-*l* sqrt-prod
7×pow1
6×sqrt-div associate-/r* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u flip3-- div-exp associate-/r/ flip-- log1p-expm1-u
3×associate-*r*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 98
Calls
4 calls:
19.0ms
(- (* z z) (* t a))
68.0ms
(* (/ (* z y) (sqrt (- (* z z) (* t a)))) x)
26.0ms
(/ (* z y) (sqrt (- (* z z) (* t a))))
20.0ms
(sqrt (- (* z z) (* t a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* t a))
121.0ms
(* (/ (* z y) (sqrt (- (* z z) (* t a)))) x)
109.0ms
(/ (* z y) (sqrt (- (* z z) (* t a))))
90.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
110 → 110
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01561666
14151543
224251355
done50011354

prune405.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes506.0ms

Accuracy

77.9% (4.7b remaining)

Error of 7.9b against oracle of 3.2b and baseline of 24.5b

bsearch519.0ms

Steps
ItersRangePoint
11
6.8410550143029e-38
1.3113650301339767e-12
1.292716185531284e-12
9
-3.113286269135709e+96
-3.4065764254652804e+90
-3.603369414995161e+90

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12829
23029
done3029

end0.0ms

sample1.7s

Algorithm
intervals
Results
712.0ms8874×body80valid
187.0ms2948×body80nan