Details

sample91.0ms

Algorithm

intervals

Results

39.0ms	287×	body	80	valid
7.0ms	94×	body	80	nan

simplify75.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
5	114
4	93
3	68
2	45
1	21
0	12

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* a t))
1.7b	(/ (* x y) (sqrt (- (* z z) (* a t))))
7.3b	(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
24.8b	(sqrt (- (* z z) (* a t)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `associate-l` `sqrt-prod`
7×	`pow1`
6×	`associate-/r*` `sqrt-div` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `flip--`
3×	`associate-r`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `associate-/l*` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

7.0ms	(- (* z z) (* a t))
21.0ms	(/ (* x y) (sqrt (- (* z z) (* a t))))
44.0ms	(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
15.0ms	(sqrt (- (* z z) (* a t)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* z z) (* a t))
130.0ms	(/ (* x y) (sqrt (- (* z z) (* a t))))
144.0ms	(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
79.0ms	(sqrt (- (* z z) (* a t)))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	2100
1	392
0	144

prune757.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* a t))
1.0b	(* (/ x 1) (/ (* y z) (sqrt (- (* z z) (* a t)))))
8.7b	(/ (* y z) (sqrt (- (* z z) (* a t))))
24.8b	(sqrt (- (* z z) (* a t)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
30×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
23×	`times-frac`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`div-exp`
13×	`associate-l` `prod-exp`
12×	`associate-r` `sqrt-prod`
9×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1`
6×	`associate-/r*` `sqrt-div` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`1-exp` `div-inv` `unswap-sqr`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `-commutative` `associate-/l`

Counts

4 → 111

Calls

4 calls:

7.0ms	(- (* z z) (* a t))
52.0ms	(* (/ x 1) (/ (* y z) (sqrt (- (* z z) (* a t)))))
31.0ms	(/ (* y z) (sqrt (- (* z z) (* a t))))
11.0ms	(sqrt (- (* z z) (* a t)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* z z) (* a t))
157.0ms	(* (/ x 1) (/ (* y z) (sqrt (- (* z z) (* a t)))))
115.0ms	(/ (* y z) (sqrt (- (* z z) (* a t))))
97.0ms	(sqrt (- (* z z) (* a t)))

simplify1.9s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	3579
1	585
0	188

prune873.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* a t))
1.0b	(* x (/ y (/ (sqrt (- (* z z) (* a t))) z)))
1.7b	(/ y (/ (sqrt (- (* z z) (* a t))) z))
24.8b	(sqrt (- (* z z) (* a t)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`*-un-lft-identity` `add-cube-cbrt`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
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×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 227

Calls

4 calls:

12.0ms	(- (* z z) (* a t))
84.0ms	(* x (/ y (/ (sqrt (- (* z z) (* a t))) z)))
39.0ms	(/ y (/ (sqrt (- (* z z) (* a t))) z))
10.0ms	(sqrt (- (* z z) (* a t)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* z z) (* a t))
187.0ms	(* x (/ y (/ (sqrt (- (* z z) (* a t))) z)))
115.0ms	(/ y (/ (sqrt (- (* z z) (* a t))) z))
82.0ms	(sqrt (- (* z z) (* a t)))

simplify686.0ms

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
1	960
0	330

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* a t))) z)
0.2b	(- (* z z) (* a t))
3.5b	(/ (* y x) (/ (sqrt (- (* z z) (* a t))) z))
24.8b	(sqrt (- (* z z) (* a t)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

29.0ms	(/ (sqrt (- (* z z) (* a t))) z)
13.0ms	(- (* z z) (* a t))
34.0ms	(/ (* y x) (/ (sqrt (- (* z z) (* a t))) z))
15.0ms	(sqrt (- (* z z) (* a t)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sqrt (- (* z z) (* a t))) z)
59.0ms	(- (* z z) (* a t))
153.0ms	(/ (* y x) (/ (sqrt (- (* z z) (* a t))) z))
497.0ms	(sqrt (- (* z z) (* a t)))

simplify1.8s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
2	3658
1	577
0	211

prune931.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

regimes607.0ms

Accuracy

78.2% (4.3b remaining)

Error of 7.6b against oracle of 3.3b and baseline of 23.0b

bsearch128.0ms

Steps

Iters	Range		Point
6	4.392987423579743e+60	5.909848464129449e+61	2.035196962814329e+61
9	-4.305487296037889e+89	-1.699884990384593e+83	-1.1052228700196578e+88

simplify11.0ms

Iterations

Iter	Nodes
done	72
4	72
3	66
2	50
1	36
0	26

end0.0ms

sample2.0s

Algorithm

intervals

Results

786.0ms	8908×	body	80	valid
366.0ms	2898×	body	80	nan