Details

sample70.0ms

Algorithm

intervals

Results

25.0ms	282×	body	80	valid
7.0ms	91×	body	80	nan

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	21	14
2	45	14
3	67	14
4	92	14
5	107	14
done	107	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite79.0ms

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×	`sqrt-div`
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` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) z)
36.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
15.0ms	(sqrt (- (* z z) (* t a)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
28.0ms	(* (* x y) z)
134.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
88.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	1237
1	341	1135
2	1495	975
done	5001	974

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
4.1b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite103.0ms

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×	`sqrt-div` `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` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

18.0ms	(/ (sqrt (- (* z z) (* t a))) z)
8.0ms	(- (* z z) (* t a))
53.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
18.0ms	(sqrt (- (* z z) (* t a)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (sqrt (- (* z z) (* t a))) z)
45.0ms	(- (* z z) (* t a))
133.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
110.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

144 → 144

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	210	2654
1	500	2421
2	1641	2221
done	5000	2218

prune493.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.3b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite122.0ms

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×	`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` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 227

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
17.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
60.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms	(sqrt (- (* z z) (* t a)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* z z) (* t a))
76.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
118.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
91.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

239 → 239

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	330	4875
1	782	4362
2	2291	4138
done	5001	4135

prune973.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.3b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.5b	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite136.0ms

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`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`

Counts

4 → 433

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
31.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
45.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
16.0ms	(sqrt (- (* z z) (* t a)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* z z) (* t a))
92.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
124.0ms	(/ x (/ (/ (sqrt (- (* z z) (* t a))) z) y))
81.0ms	(sqrt (- (* z z) (* t a)))

simplify3.3s

Counts

445 → 445

Iterations

Useful iterations: 2 (2.1s)

Iter	Nodes	Cost
0	656	12287
1	1519	11278
2	4755	10862
done	5000	10862

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

regimes526.0ms

Accuracy

85.1% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 23.1b

bsearch167.0ms

Steps

Iters	Range		Point
9	6.663579023451854e+147	9.351805393147033e+156	1.4268392759836289e+149
9	-1.0782077558969122e+127	-3.292378933949146e+117	-1.08880382076931e+119

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	26	29
2	28	29
done	28	29

end0.0ms

sample2.2s

Algorithm

intervals

Results

708.0ms	8845×	body	80	valid
249.0ms	3033×	body	80	nan