Details

sample69.0ms

Algorithm

intervals

Results

37.0ms	286×	body	80	valid
10.0ms	95×	body	80	nan

simplify92.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	103
6	103
5	97
4	70
3	53
2	36
1	21
0	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.7b	(* (* x y) z)
6.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
47.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* z z) (* t a))
47.0ms	(* (* x y) z)
143.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
98.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1429
1	362
0	138

prune648.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.0b	(- (* z z) (* t a))
3.2b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
24×	`associate-r` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `sqrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `insert-posit16` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `associate-r/` `-commutative`

Counts

4 → 116

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
58.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
16.0ms	(sqrt (- (* z z) (* t a)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ z (sqrt (- (* z z) (* t a))))
42.0ms	(- (* z z) (* t a))
120.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
76.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

128 → 128

Iterations

Iter	Nodes
done	5003
2	1661
1	476
0	171

prune659.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
1.0b	(- (* z z) (* t a))
3.2b	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
32×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
27×	`prod-exp`
25×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`pow1` `add-cube-cbrt`
15×	`cbrt-unprod`
14×	`sqrt-prod`
9×	`pow-prod-down`
6×	`div-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`sqrt-div` `associate-l` `associate-*r/` `insert-posit16`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--`
2×	`associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 112

Calls

4 calls:

37.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
14.0ms	(- (* z z) (* t a))
74.0ms	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
7.0ms	(sqrt (- (* z z) (* t a)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
48.0ms	(- (* z z) (* t a))
100.0ms	(* (* y x) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
104.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5003
2	1578
1	493
0	184

prune717.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
1.0b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
2.6b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`associate-l`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`sqrt-div` `associate-r` `pow-prod-down` `insert-posit16`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
40.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
44.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
14.0ms	(sqrt (- (* z z) (* t a)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* z z) (* t a))
110.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
98.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
93.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5005
2	1259
1	390
0	157

prune597.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.2b

regimes760.0ms

Accuracy

85.5% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 22.3b

bsearch140.0ms

Steps

Iters	Range		Point
9	1.3811436676451923e+110	7.486911991823205e+115	1.1848486164183457e+114
7	-2.513744904282275e+156	-1.854306054422796e+154	-1.8913959868564195e+154

simplify11.0ms

Iterations

Iter	Nodes
done	33
2	33
1	30
0	22

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	8876×	body	80	valid
293.0ms	2933×	body	80	nan