Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	281×	body	80	valid
7.0ms	93×	body	80	nan

simplify145.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.7b	(* (* x y) z)
8.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.7b	(sqrt (- (* z z) (* t a)))

rewrite157.0ms

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)
73.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.0ms	(sqrt (- (* z z) (* t a)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* z z) (* t a))
52.0ms	(* (* x y) z)
195.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
132.0ms	(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

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

prune950.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
2.6b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
27.7b	(sqrt (- (* z z) (* t a)))

rewrite141.0ms

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:

41.0ms	(/ (sqrt (- (* z z) (* t a))) z)
18.0ms	(- (* z z) (* t a))
46.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.0ms	(sqrt (- (* z z) (* t a)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (sqrt (- (* z z) (* t a))) z)
76.0ms	(- (* z z) (* t a))
200.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
123.0ms	(sqrt (- (* z z) (* t a)))

simplify3.9s

Counts

154 → 154

Iterations

Useful iterations: done (3.9s)

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

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.7b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
27.7b	(sqrt (- (* z z) (* t a)))

rewrite214.0ms

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:

26.0ms	(- (* z z) (* t a))
96.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
43.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
24.0ms	(sqrt (- (* z z) (* t a)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* z z) (* t a))
203.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
126.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
151.0ms	(sqrt (- (* z z) (* t a)))

simplify917.0ms

Counts

249 → 249

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	342	4983
1	974	4546
done	5000	4285

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
1.7b	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
27.7b	(sqrt (- (* z z) (* t a)))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
91×	`add-sqr-sqrt`
72×	`-un-lft-identity` `associate-r*`
69×	`add-cube-cbrt`
51×	`add-exp-log`
32×	`sqrt-prod`
27×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
12×	`pow1`
10×	`cbrt-unprod`
7×	`unswap-sqr`
6×	`cbrt-undiv` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv`
2×	`flip3--` `sqrt-div` `un-div-inv` `*-commutative` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 167

Calls

4 calls:

21.0ms	(- (* z z) (* t a))
143.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
127.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
28.0ms	(sqrt (- (* z z) (* t a)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* z z) (* t a))
222.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
155.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
155.0ms	(sqrt (- (* z z) (* t a)))

simplify2.9s

Counts

179 → 179

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	300	3141
1	894	2691
2	3989	2232
done	5000	2221

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

regimes1.0s

Accuracy

85.2% (2.9b remaining)

Error of 6.4b against oracle of 3.5b and baseline of 23.2b

bsearch178.0ms

Steps

Iters	Range		Point
7	4.67750069922532e+95	7.025739250020152e+97	6.4447789061204586e+97
7	-1.5468273757251828e+156	-9.96161025005455e+153	-1.015321300934204e+154

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	31
1	31	31
2	34	31
done	34	31

end0.0ms

sample2.2s

Algorithm

intervals

Results

927.0ms	8842×	body	80	valid
197.0ms	2877×	body	80	nan