Details

sample60.0ms

Algorithm

intervals

Results

17.0ms	283×	body	80	valid
8.0ms	81×	body	80	nan

simplify122.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
6.0b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite75.0ms

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` `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 → 86

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) z)
30.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms	(sqrt (- (* z z) (* t a)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* z z) (* t a))
42.0ms	(* (* x y) z)
107.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
85.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2299
1	385
0	146

prune687.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.8b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite100.0ms

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/` `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 → 122

Calls

4 calls:

22.0ms	(/ z (sqrt (- (* z z) (* t a))))
13.0ms	(- (* z z) (* t a))
46.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ z (sqrt (- (* z z) (* t a))))
44.0ms	(- (* z z) (* t a))
142.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
94.0ms	(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	3165
1	496
0	179

prune937.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.8b	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
24.1b	(cbrt (- (* z z) (* t a)))
24.1b	(cbrt (- (* z z) (* t a)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
16×	`add-cbrt-cube`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `pow1/3` `div-exp` `associate-*r/`
1×	`sub-neg` `fma-neg` `diff-log` `associate-r` `prod-diff` `*-commutative`

Counts

4 → 71

Calls

4 calls:

14.0ms	(- (* z z) (* t a))
53.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
9.0ms	(cbrt (- (* z z) (* t a)))
9.0ms	(cbrt (- (* z z) (* t a)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* z z) (* t a))
214.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
126.0ms	(cbrt (- (* z z) (* t a)))
139.0ms	(cbrt (- (* z z) (* t a)))

simplify1.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1712
1	412
0	151

prune712.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.1b	(* x (/ z (sqrt (- (* z z) (* t a)))))
2.1b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite150.0ms

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` `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 → 102

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
35.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
77.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
18.0ms	(sqrt (- (* z z) (* t a)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* z z) (* t a))
92.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
117.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
90.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1910
1	457
0	174

prune648.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes1.3s

Accuracy

83.1% (3.4b remaining)

Error of 6.9b against oracle of 3.4b and baseline of 23.6b

bsearch149.0ms

Steps

Iters	Range		Point
7	4.962524782877993e+148	5.8027159941114316e+150	5.492884630545356e+148
10	-5.3387252649757745e+174	-1.6115166414884948e+164	-1.6311711944705693e+164

simplify10.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8857×	body	80	valid
159.0ms	2816×	body	80	nan