Details

sample86.0ms

Algorithm

intervals

Results

45.0ms	285×	body	80	valid
14.0ms	97×	body	80	nan

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	106
6	106
5	97
4	77
3	58
2	37
1	22
0	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
6.2b	(* (* x y) z)
9.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.0b	(sqrt (- (* z z) (* t a)))

rewrite78.0ms

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×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

11.0ms	(- (* z z) (* t a))
30.0ms	(* (* x y) z)
26.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms	(sqrt (- (* z z) (* t a)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* z z) (* t a))
36.0ms	(* (* x y) z)
109.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1508
1	385
0	150

prune713.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
3.3b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
24.0b	(sqrt (- (* z z) (* t a)))

rewrite116.0ms

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×	`expm1-log1p-u` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `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` `fma-neg` `diff-log` `associate-l` `prod-diff` `associate-r/` `-commutative`

Counts

4 → 126

Calls

4 calls:

25.0ms	(/ z (sqrt (- (* z z) (* t a))))
21.0ms	(- (* z z) (* t a))
56.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(sqrt (- (* z z) (* t a)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ z (sqrt (- (* z z) (* t a))))
64.0ms	(- (* z z) (* t a))
143.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
101.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1799
1	501
0	183

prune693.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
3.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.0b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

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×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 146

Calls

4 calls:

15.0ms	(/ (sqrt (- (* z z) (* t a))) z)
12.0ms	(- (* z z) (* t a))
25.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
11.0ms	(sqrt (- (* z z) (* t a)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (sqrt (- (* z z) (* t a))) z)
53.0ms	(- (* z z) (* t a))
121.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
108.0ms	(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts

158 → 158

Iterations

Iter	Nodes
done	5013
2	1959
1	588
0	226

prune928.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
2.0b	(* x (/ z (sqrt (- (* z z) (* t a)))))
2.2b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
24.0b	(sqrt (- (* z z) (* t a)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
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×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 106

Calls

4 calls:

14.0ms	(- (* z z) (* t a))
37.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
66.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* z z) (* t a))
106.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
124.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
85.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1446
1	444
0	178

prune675.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.3b

regimes823.0ms

Accuracy

76% (4.6b remaining)

Error of 7.7b against oracle of 3.1b and baseline of 22.2b

bsearch251.0ms

Steps

Iters	Range		Point
9	3.7535787772274716e+35	3.0457229073637325e+41	1.1088800579390318e+41
10	-1.3003845913939003e+48	-2.2741946568354854e+34	-1.0884743696281288e+48

simplify7.0ms

Iterations

Iter	Nodes
done	30
2	30
1	27
0	21

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.8s	8828×	body	80	valid
414.0ms	3015×	body	80	nan