Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

276×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(+ (* a c) (* b d))
43.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* a c) (* b d))
137.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5002
3	2527
2	777
1	235
0	83

prune324.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
15.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

11.0ms	(+ (* a c) (* b d))
25.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* a c) (* b d))
140.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	2246
2	768
1	278
0	114

prune525.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
15.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

7.0ms	(+ (* a c) (* b d))
25.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* a c) (* b d))
165.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.5s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	2246
2	768
1	278
0	114

prune472.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize29.0ms

Local error

Found 4 expressions with local error:

15.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

25.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
11.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
3	1891
2	659
1	249
0	105

prune487.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.3b

regimes303.0ms

Accuracy

-13.7% (3.4b remaining)

Error of 26.3b against oracle of 22.9b and baseline of 25.9b

bsearch27.0ms

Steps

Iters	Range		Point
5	1.34232255763024e+37	2.8506796103821506e+37	2.814854621501251e+37

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample980.0ms

Algorithm

intervals

Results

757.0ms

8473×

body

valid