Details

Time bar (total: 8.2s)

sample31.0ms

Algorithm
intervals
Results
10.0ms280×body80valid
6.0ms93×body80nan

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36814
49214
510514
done10514

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize12.0ms

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)))

rewrite28.0ms

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))))
5.0ms
(sqrt (- (* z z) (* t a)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
79.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify541.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (175.0ms)

IterNodesCost
01461331
13631220
216431062
done50001062

prune281.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
11.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
5.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
83.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify645.0ms

Counts
154 → 154
Iterations

Useful iterations: 2 (254.0ms)

IterNodesCost
02222758
15392513
217892320
done50002320

prune408.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative
Counts
4 → 237
Calls
4 calls:
10.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
39.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
3.0ms
(- (* z z) (* t a))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
84.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
32.0ms
(- (* z z) (* t a))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
249 → 249
Iterations

Useful iterations: 2 (337.0ms)

IterNodesCost
03424983
18354462
224114239
done50014239

prune651.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
1.0b
(- (* z z) (* t a))
1.3b
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
828×times-frac
400×add-sqr-sqrt
399×add-cube-cbrt *-un-lft-identity
147×sqrt-prod
73×associate-/r*
25×associate-/l*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/ associate-/l/
Counts
4 → 443
Calls
4 calls:
12.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
3.0ms
(- (* z z) (* t a))
25.0ms
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
4.0ms
(sqrt (- (* z z) (* t a)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
33.0ms
(- (* z z) (* t a))
83.0ms
(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
455 → 455
Iterations

Useful iterations: done (1.0s)

IterNodesCost
066812395
1164411376
done500011111

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.3b

regimes341.0ms

Accuracy

84.7% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 22.3b

bsearch82.0ms

Steps
ItersRangePoint
7
4.43464859477407e+147
1.5123157394476474e+149
6.926066888201142e+147
9
-2.7283838574175814e+156
-2.1161453073457986e+149
-8.618354790122042e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12729
22929
done2929

end0.0ms

sample784.0ms

Algorithm
intervals
Results
344.0ms8864×body80valid
100.0ms2952×body80nan