Details

Time bar (total: 14.5s)

sample50.0ms

Algorithm
intervals
Results
17.0ms276×body80valid
5.0ms88×body80nan

simplify113.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37314
49814
511914
done11914

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize19.0ms

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)))

rewrite136.0ms

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:
18.0ms
(- (* z z) (* t a))
36.0ms
(* (* x y) z)
65.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
39.0ms
(* (* x y) z)
134.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
115.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01461331
13861225
222651080
done50001077

prune494.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
29.0ms
(/ z (sqrt (- (* z z) (* t a))))
9.0ms
(- (* z z) (* t a))
80.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
24.0ms
(sqrt (- (* z z) (* t a)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ z (sqrt (- (* z z) (* t a))))
56.0ms
(- (* z z) (* t a))
127.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
91.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
134 → 134
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01792135
14971953
232151754
done50001749

prune578.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.2b
(* x (/ z (sqrt (- (* z z) (* t a)))))
1.3b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite149.0ms

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×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
18.0ms
(- (* z z) (* t a))
48.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
64.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
12.0ms
(sqrt (- (* z z) (* t a)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* z z) (* t a))
95.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
111.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
86.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
114 → 114
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01741680
14581565
219061354
done50001353

prune489.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

localize36.0ms

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)))

rewrite74.0ms

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 expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
18.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
22.0ms
(sqrt (- (* z z) (* t a)))
17.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
107.0ms
(sqrt (- (* z z) (* t a)))
92.0ms
(sqrt (- (* z z) (* t a)))
85.0ms
(sqrt (- (* z z) (* t a)))

simplify2.8s

Counts
98 → 98
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01531602
12981459
29341357
343711347
done50001347

prune443.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.8b

regimes350.0ms

Accuracy

86.1% (2.7b remaining)

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

bsearch149.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12829
23029
done3029

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.0s8885×body80valid
273.0ms2899×body80nan