Details

sample337.0ms

Algorithm

intervals

Results

127.0ms	283×	body	80	valid
7.0ms	83×	body	80	nan

simplify295.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	101
6	101
5	92
4	72
3	53
2	36
1	21
0	12

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
10.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
38.0ms	(* (* x y) z)
259.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
50.0ms	(sqrt (- (* z z) (* t a)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (* z z) (* t a))
47.0ms	(* (* x y) z)
223.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
316.0ms	(sqrt (- (* z z) (* t a)))

simplify5.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5004
2	1450
1	360
0	134

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize393.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.3b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

41.0ms	(/ z (sqrt (- (* z z) (* t a))))
47.0ms	(- (* z z) (* t a))
89.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ z (sqrt (- (* z z) (* t a))))
80.0ms	(- (* z z) (* t a))
178.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
142.0ms	(sqrt (- (* z z) (* t a)))

simplify5.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1773
1	473
0	166

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

15.0ms	(- (* z z) (* t a))
76.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
95.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
18.0ms	(sqrt (- (* z z) (* t a)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (* z z) (* t a))
217.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
167.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify4.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1363
1	425
0	161

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
2.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.4b	(sqrt (- (* z z) (* t a)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

37.0ms	(/ (sqrt (- (* z z) (* t a))) z)
17.0ms	(- (* z z) (* t a))
73.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
18.0ms	(sqrt (- (* z z) (* t a)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (sqrt (- (* z z) (* t a))) z)
72.0ms	(- (* z z) (* t a))
209.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
138.0ms	(sqrt (- (* z z) (* t a)))

simplify5.2s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1899
1	558
0	210

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

regimes2.8s

Accuracy

86% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 23.1b

bsearch381.0ms

Steps

Iters	Range		Point
9	1.6100917271418707e+137	6.896997489231346e+142	2.6835052906232983e+137
10	-2.473174617620054e+121	-1.6898447500521535e+111	-2.6901132879983587e+113

simplify11.0ms

Iterations

Iter	Nodes
done	29
2	29
1	26
0	21

end0.0ms

sample5.7s

Algorithm

intervals

Results

4.0s	8840×	body	80	valid
769.0ms	2973×	body	80	nan