Details

Time bar (total: 13.3s)

sample40.0ms

Algorithm
intervals
Results
14.0ms284×body80valid
4.0ms96×body80nan

simplify68.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize27.0ms

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)))

rewrite121.0ms

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:
14.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) z)
54.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms
(sqrt (- (* z z) (* t a)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
135.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
97.0ms
(sqrt (- (* z z) (* t a)))

simplify908.0ms

Counts
88 → 88

prune369.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize22.0ms

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) (sqrt 1)) (/ z (sqrt (- (* z z) (* t a)))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
27×add-exp-log add-cbrt-cube
24×associate-*r*
10×associate-*l*
8×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1
6×sqrt-div associate-/r* add-log-exp
4×flip3-- associate-/r/ flip--
3×div-inv associate-/l* unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 129
Calls
4 calls:
15.0ms
(/ z (sqrt (- (* z z) (* t a))))
15.0ms
(- (* z z) (* t a))
75.0ms
(* (/ (* x y) (sqrt 1)) (/ z (sqrt (- (* z z) (* t a)))))
22.0ms
(sqrt (- (* z z) (* t a)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ z (sqrt (- (* z z) (* t a))))
48.0ms
(- (* z z) (* t a))
134.0ms
(* (/ (* x y) (sqrt 1)) (/ z (sqrt (- (* z z) (* t a)))))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
141 → 141

prune743.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize16.0ms

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) (sqrt 1)) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
45×add-cbrt-cube
36×prod-exp
35×add-sqr-sqrt
28×times-frac
25×associate-*r*
24×*-un-lft-identity
22×add-cube-cbrt
20×cbrt-unprod
18×div-exp
17×sqrt-prod
13×associate-*l*
12×pow1
10×cbrt-undiv
6×add-log-exp
5×associate-*r/ unswap-sqr
4×rec-exp sqrt-div 1-exp pow-prod-down
3×flip3-- un-div-inv flip--
2×frac-times associate-/r/ *-commutative div-inv
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*l/
Counts
4 → 126
Calls
4 calls:
61.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
8.0ms
(- (* z z) (* t a))
147.0ms
(* (/ (* x y) (sqrt 1)) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
11.0ms
(sqrt (- (* z z) (* t a)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
66.0ms
(- (* z z) (* t a))
166.0ms
(* (/ (* x y) (sqrt 1)) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
89.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
138 → 138

prune512.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
2.9b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
32.0ms
(/ (sqrt (- (* z z) (* t a))) z)
16.0ms
(- (* z z) (* t a))
41.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
17.0ms
(sqrt (- (* z z) (* t a)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (sqrt (- (* z z) (* t a))) z)
52.0ms
(- (* z z) (* t a))
120.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
95.0ms
(sqrt (- (* z z) (* t a)))

simplify956.0ms

Counts
144 → 144

prune621.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.4b

regimes351.0ms

Accuracy

84.5% (3.0b remaining)

Error of 6.1b against oracle of 3.1b and baseline of 22.6b

bsearch93.0ms

Steps
ItersRangePoint
4
1.5523497138925845e+121
2.2438624246711994e+121
2.130897152856616e+121
8
-4.4687952358618183e+136
-2.295024957636829e+132
-4.4038128116553484e+136

simplify1.6s

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s8851×body80valid
222.0ms2869×body80nan