Details

sample43.0ms

Algorithm

intervals

Results

16.0ms	282×	body	80	valid
5.0ms	102×	body	80	nan

simplify80.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
6.1b	(* (* x y) z)
11.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

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:

7.0ms	(- (* z z) (* t a))
14.0ms	(* (* x y) z)
31.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms	(sqrt (- (* z z) (* t a)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* z z) (* t a))
36.0ms	(* (* x y) z)
150.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
106.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2299
1	385
0	146

prune798.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
3.8b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.0b	(sqrt (- (* z z) (* t a)))

rewrite104.0ms

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))
48.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ z (sqrt (- (* z z) (* t a))))
39.0ms	(- (* z z) (* t a))
97.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify2.6s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	3165
1	496
0	179

prune803.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
23.8b	(cbrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt z)
49.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
5.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt z)
291.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
129.0ms	(cbrt (- (* z z) (* t a)))
121.0ms	(cbrt (- (* z z) (* t a)))

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1821
1	417
0	151

prune839.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.3b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
23.0b	(sqrt (- (* z z) (* t a)))
23.0b	(sqrt (- (* z z) (* t a)))
23.8b	(cbrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
16×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `div-exp` `associate-*r/`
1×	`pow1/3` `associate-r` `*-commutative`

Counts

4 → 74

Calls

4 calls:

52.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
10.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(cbrt (- (* z z) (* t a)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* y (* x (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
88.0ms	(sqrt (- (* z z) (* t a)))
93.0ms	(sqrt (- (* z z) (* t a)))
107.0ms	(cbrt (- (* z z) (* t a)))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1776
1	435
0	162

prune941.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.3b

regimes1.5s

Accuracy

86.8% (2.5b remaining)

Error of 5.8b against oracle of 3.3b and baseline of 22.3b

bsearch159.0ms

Steps

Iters	Range		Point
8	4.271611683557293e+96	5.363233345281319e+99	1.239440162778037e+98
7	-1.0846037281689326e+122	-1.7535874949385931e+120	-4.828914214900402e+120

simplify9.0ms

Iterations

Iter	Nodes
done	47
2	47
1	45
0	35

end0.0ms

sample1.9s

Algorithm

intervals

Results

786.0ms	8855×	body	80	valid
577.0ms	2804×	body	80	nan