Details

Time bar (total: 15.2s)

sample60.0ms

Algorithm
intervals
Results
20.0ms276×body80valid
6.0ms95×body80nan

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
4.2b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite138.0ms

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:
19.0ms
(- (* z z) (* t a))
36.0ms
(* (* x y) z)
47.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
31.0ms
(sqrt (- (* z z) (* t a)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
32.0ms
(* (* x y) z)
101.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
85.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
98 → 98
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune459.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
2.8b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite140.0ms

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))))
20.0ms
(- (* z z) (* t a))
70.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ z (sqrt (- (* z z) (* t a))))
45.0ms
(- (* z z) (* t a))
128.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
104.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
134 → 134
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01792135
14381941
215821740
done50001738

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* y x) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
25.2b
(sqrt (- (* z z) (* t a)))
25.2b
(sqrt (- (* z z) (* t a)))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
23×prod-exp cbrt-unprod
18×sqrt-div
13×associate-*r*
12×pow1 cbrt-div
11×add-sqr-sqrt
9×flip3-- sqrt-prod flip--
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp associate-/r/
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
2×associate-*l/
1×times-frac associate-*l* *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
163.0ms
(* (* y x) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
11.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))
14.0ms
(sqrt (- (* z z) (* t a)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(* (* y x) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
114.0ms
(sqrt (- (* z z) (* t a)))
83.0ms
(sqrt (- (* z z) (* t a)))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
110 → 110
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01622655
14762406
220901868
done50011734

prune620.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(* x (/ z (sqrt (- (* z z) (* t a)))))
1.2b
(- (* z z) (* t a))
2.6b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite168.0ms

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:
71.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(- (* z z) (* t a))
67.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
15.0ms
(sqrt (- (* z z) (* t a)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(- (* z z) (* t a))
134.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify3.0s

Counts
114 → 114
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01741680
14141552
212121354
340401340
done50001340

prune528.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.9b

regimes373.0ms

Accuracy

84.5% (2.9b remaining)

Error of 6.3b against oracle of 3.5b and baseline of 21.9b

bsearch125.0ms

Steps
ItersRangePoint
7
7.763235271532398e+95
1.3510080551639932e+97
1.1719295172753232e+97
9
-7.754247409175047e+159
-6.278022273170321e+153
-1.3401354470987563e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02657
13357
23557
done3557

end0.0ms

sample1.9s

Algorithm
intervals
Results
733.0ms8875×body80valid
244.0ms2953×body80nan