Details

Time bar (total: 8.9s)

sample31.0ms

Algorithm
intervals
Results
11.0ms276×body80valid
3.0ms101×body80nan

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24414
36514
48914
510214
done10214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
7.3b
(* (* x y) z)
9.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

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:
2.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
100.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify913.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (179.0ms)

IterNodesCost
01341237
13431135
21586975
done5001975

prune260.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
3.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ z (sqrt (- (* z z) (* t a))))
38.0ms
(- (* z z) (* t a))
100.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify900.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (276.0ms)

IterNodesCost
01662031
14291847
216521643
done50001643

prune327.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.0b
(- (* z z) (* t a))
1.5b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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:
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
20.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
38.0ms
(- (* z z) (* t a))
98.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
104 → 104
Iterations

Useful iterations: 3 (868.0ms)

IterNodesCost
01611572
14011453
211831241
343151240
done50001240

prune274.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
25.0b
(sqrt (- (* z z) (* t a)))
25.0b
(sqrt (- (* z z) (* t a)))
25.0b
(sqrt (- (* z z) (* t a)))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
46×add-cbrt-cube
43×prod-exp cbrt-unprod
16×pow1
14×cbrt-undiv div-exp
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div associate-*r/ pow-prod-down
4×add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* flip--
1×frac-times associate-*r* associate-*l/ *-commutative
Counts
4 → 89
Calls
4 calls:
382.0ms
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
67.0ms
(sqrt (- (* z z) (* t a)))
70.0ms
(sqrt (- (* z z) (* t a)))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify876.0ms

Counts
101 → 101
Iterations

Useful iterations: done (872.0ms)

IterNodesCost
01803393
16253144
225701624
done50001612

prune363.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes344.0ms

Accuracy

85.8% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 22.8b

bsearch108.0ms

Steps
ItersRangePoint
9
1.5599000651954472e+122
3.251841885581708e+128
2.2349389384476415e+125
9
-8.382253253648058e+154
-1.005629218284056e+149
-9.341949798077739e+151

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12729
23029
done3029

end0.0ms

sample835.0ms

Algorithm
intervals
Results
358.0ms8886×body80valid
102.0ms2944×body80nan