Details

Time bar (total: 9.6s)

sample30.0ms

Algorithm
intervals
Results
11.0ms280×body80valid
3.0ms93×body80nan

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36914
49314
510614
done10614

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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:
3.0ms
(- (* 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)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify599.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
01461331
13721224
218061062
done50001062

prune287.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
2.4b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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:
6.0ms
(/ 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)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
34.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify768.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (160.0ms)

IterNodesCost
01782135
14581955
220351740
done50011740

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.0b
(- (* z z) (* t a))
22.0b
(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×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:
19.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
34.0ms
(- (* z z) (* t a))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify604.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
01731680
14291558
216781342
done50011342

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
22.9b
(cbrt (- (* z z) (* t a)))
22.9b
(cbrt (- (* z z) (* t a)))
22.9b
(cbrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 97
Calls
4 calls:
33.0ms
(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
2.0ms
(cbrt (- (* z z) (* t a)))
6.0ms
(cbrt (- (* z z) (* t a)))
3.0ms
(cbrt (- (* z z) (* t a)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (* (* (cbrt (- (* z z) (* t a))) (cbrt (- (* z z) (* t a)))) (cbrt (- (* z z) (* t a)))))
82.0ms
(cbrt (- (* z z) (* t a)))
81.0ms
(cbrt (- (* z z) (* t a)))
82.0ms
(cbrt (- (* z z) (* t a)))

simplify3.6s

Counts
109 → 109
Iterations

Useful iterations: 3 (556.0ms)

IterNodesCost
01873217
13432786
28952203
337022138
done50002138

prune342.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.3b

regimes547.0ms

Accuracy

83% (3.2b remaining)

Error of 6.5b against oracle of 3.3b and baseline of 22.4b

bsearch90.0ms

Steps
ItersRangePoint
7
4.43464859477407e+147
1.5123157394476474e+149
1.124903159705272e+148
9
-5.96846737894306e+65
-7.547141837029504e+58
-5.1201051050426465e+65

simplify5.0ms

Iterations

Useful iterations: 2 (2.0ms)

IterNodesCost
02543
13341
23840
34940
done4940

end0.0ms

sample835.0ms

Algorithm
intervals
Results
361.0ms8864×body80valid
104.0ms2952×body80nan