Details

sample74.0ms

Algorithm

intervals

Results

26.0ms	288×	body	80	valid
6.0ms	72×	body	80	nan

simplify146.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
9.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite110.0ms

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))
18.0ms	(* (* x y) z)
45.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
32.0ms	(sqrt (- (* z z) (* t a)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* z z) (* t a))
44.0ms	(* (* x y) z)
113.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
94.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: done (1.4s)

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

prune493.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
2.8b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite114.0ms

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:

37.0ms	(/ (sqrt (- (* z z) (* t a))) z)
18.0ms	(- (* z z) (* t a))
25.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
27.0ms	(sqrt (- (* z z) (* t a)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sqrt (- (* z z) (* t a))) z)
47.0ms	(- (* z z) (* t a))
137.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
95.0ms	(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts

154 → 154

Iterations

Useful iterations: done (2.2s)

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

prune531.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.2b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite136.0ms

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:

9.0ms	(- (* z z) (* t a))
18.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
72.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
12.0ms	(sqrt (- (* z z) (* t a)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* z z) (* t a))
70.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
111.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify632.0ms

Counts

249 → 249

Iterations

Useful iterations: done (622.0ms)

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

prune903.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
1.1b	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
2.2b	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
24.9b	(sqrt (- (* z z) (* t a)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

268×	`times-frac`
166×	`add-sqr-sqrt`
147×	`*-un-lft-identity`
144×	`add-cube-cbrt`
72×	`associate-r`
68×	`sqrt-prod`
62×	`add-exp-log`
32×	`add-cbrt-cube`
22×	`prod-exp` `associate-/r*`
21×	`div-exp`
13×	`pow1`
10×	`cbrt-unprod`
9×	`cbrt-undiv` `div-inv`
7×	`unswap-sqr`
6×	`rec-exp` `1-exp` `associate-l`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`sqrt-div` `associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `flip3--` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `inv-pow`

Counts

4 → 265

Calls

4 calls:

30.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
77.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
89.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
13.0ms	(sqrt (- (* z z) (* t a)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
75.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
135.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify2.5s

Counts

277 → 277

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	344	5647
1	1002	4738
2	4508	4251
done	5000	4250

prune854.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes456.0ms

Accuracy

84.2% (3.1b remaining)

Error of 6.4b against oracle of 3.3b and baseline of 22.9b

bsearch113.0ms

Steps

Iters	Range		Point
8	1.473270777738138e+80	6.009375374018846e+83	6.239560565980057e+82
7	-6.537164733756459e+138	-2.8278494132354943e+136	-8.271419220344132e+137

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	31
1	32	31
2	34	31
done	34	31

end0.0ms

sample1.8s

Algorithm

intervals

Results

605.0ms	8817×	body	80	valid
203.0ms	2946×	body	80	nan