Details

sample72.0ms

Algorithm

intervals

Results

25.0ms	288×	body	80	valid
9.0ms	111×	body	80	nan

simplify132.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	22	14
2	46	14
3	73	14
4	98	14
5	119	14
done	119	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* z z) (* t a))
6.1b	(* (* x y) z)
10.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite121.0ms

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:

9.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
62.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.0ms	(sqrt (- (* z z) (* t a)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* z z) (* t a))
36.0ms	(* (* x y) z)
117.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
82.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	146	1331
1	386	1225
2	2265	1080
done	5000	1077

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.4b	(- (* z z) (* t a))
2.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite111.0ms

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:

34.0ms	(/ (sqrt (- (* z z) (* t a))) z)
17.0ms	(- (* z z) (* t a))
37.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (sqrt (- (* z z) (* t a))) z)
63.0ms	(- (* z z) (* t a))
162.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
112.0ms	(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts

154 → 154

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	222	2758
1	592	2536
2	3659	2332
done	5001	2330

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.1b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.4b	(- (* z z) (* t a))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite135.0ms

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:

18.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
69.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
18.0ms	(- (* z z) (* t a))
16.0ms	(sqrt (- (* z z) (* t a)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
116.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
52.0ms	(- (* z z) (* t a))
92.0ms	(sqrt (- (* z z) (* t a)))

simplify709.0ms

Counts

249 → 249

Iterations

Useful iterations: done (701.0ms)

Iter	Nodes	Cost
0	342	4983
1	978	4550
done	5000	4285

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
1.4b	(- (* z z) (* t a))
2.6b	(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

296×	`times-frac`
115×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
60×	`add-exp-log`
57×	`sqrt-prod`
34×	`div-exp` `add-cbrt-cube`
27×	`associate-/r*`
25×	`associate-/l*`
17×	`cbrt-undiv`
12×	`div-inv`
8×	`prod-exp`
6×	`pow1` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 241

Calls

4 calls:

44.0ms	(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
10.0ms	(- (* z z) (* t a))
46.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
21.0ms	(sqrt (- (* z z) (* t a)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) (* x y)))
52.0ms	(- (* z z) (* t a))
182.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) (* x y))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify2.5s

Counts

253 → 253

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	371	5844
1	1053	5211
2	4635	4848
done	5000	4846

prune733.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.9b

regimes898.0ms

Accuracy

82.9% (3.3b remaining)

Error of 6.5b against oracle of 3.2b and baseline of 22.3b

bsearch114.0ms

Steps

Iters	Range		Point
7	3.43844385074201e+94	8.277117556425678e+96	8.145165494197675e+96
8	-7.309216621971448e+158	-3.5968182036650633e+155	-3.6428531200356316e+155

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	27	29
2	29	29
done	29	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

859.0ms	8829×	body	80	valid
241.0ms	2932×	body	80	nan