Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	277×	body	80	valid
5.0ms	101×	body	80	nan

simplify80.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
5	114
4	93
3	68
2	45
1	21
0	12

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
4.7b	(* (* x y) z)
8.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite71.0ms

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`
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 → 76

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
21.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* z z) (* t a))
44.0ms	(* (* x y) z)
141.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
87.0ms	(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2365
1	368
0	134

prune625.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
2.5b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite89.0ms

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×	`sqrt-div` `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` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

25.0ms	(/ (sqrt (- (* z z) (* t a))) z)
12.0ms	(- (* z z) (* t a))
31.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
13.0ms	(sqrt (- (* z z) (* t a)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sqrt (- (* z z) (* t a))) z)
50.0ms	(- (* z z) (* t a))
111.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3679
1	574
0	210

prune906.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize35.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))
23.4b	(sqrt (- (* z z) (* t a)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 76

Calls

4 calls:

5.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
10.0ms	(sqrt (- (* z z) (* t a)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
85.0ms	(sqrt (- (* z z) (* t a)))
100.0ms	(sqrt (- (* z z) (* t a)))
105.0ms	(sqrt (- (* z z) (* t a)))

simplify2.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
3	3817
2	846
1	282
0	143

prune770.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.0b

localize82.0ms

Local error

Found 4 expressions with local error:

23.4b	(sqrt (- (* z z) (* a t)))
23.4b	(sqrt (- (* z z) (* a t)))
23.4b	(sqrt (- (* z z) (* t a)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (- (* z z) (* a t)))
12.0ms	(sqrt (- (* z z) (* a t)))
7.0ms	(sqrt (- (* z z) (* t a)))
7.0ms	(sqrt (- (* z z) (* t a)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (- (* z z) (* a t)))
98.0ms	(sqrt (- (* z z) (* a t)))
81.0ms	(sqrt (- (* z z) (* t a)))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3231
2	689
1	216
0	83

prune759.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.0b

regimes1.1s

Accuracy

85.1% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 22.7b

bsearch142.0ms

Steps

Iters	Range		Point
8	3.5533055332411143e+130	3.804563911228799e+134	2.7405676072746077e+132
8	-6.974394801174976e+154	-1.8034708975126624e+151	-5.1995172941306935e+153

simplify8.0ms

Iterations

Iter	Nodes
done	32
2	32
1	29
0	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

849.0ms	8798×	body	80	valid
224.0ms	2980×	body	80	nan