Details

sample41.0ms

Algorithm

intervals

Results

29.0ms

274×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(+ (* a c) (* b d))
22.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

6.0ms	(+ (* c c) (* d d))
10.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* c c) (* d d))
38.0ms	(+ (* a c) (* b d))
103.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.4s

Counts

62 → 62

Iterations

Iter	Nodes
3	3935
2	1038
1	278
0	96

prune577.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
12.8b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))

rewrite46.0ms

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:

6.0ms	(+ (* a c) (* b d))
24.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
5.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* a c) (* b d))
118.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
44.0ms	(sqrt (+ (* c c) (* d d)))

simplify724.0ms

Counts

96 → 96

Iterations

Iter	Nodes
3	2198
2	755
1	277
0	114

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
12.9b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

11.0ms	(+ (* a c) (* b d))
48.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
5.0ms	(sqrt (+ (* c c) (* d d)))
5.0ms	(sqrt (+ (* c c) (* d d)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* a c) (* b d))
157.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
58.0ms	(sqrt (+ (* c c) (* d d)))
50.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.8s

Counts

106 → 106

Iterations

Iter	Nodes
3	4215
2	1389
1	398
0	143

prune1.0s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.7b

localize36.0ms

Local error

Found 4 expressions with local error:

12.8b	(/ (+ (* a c) (* b d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
10×	`flip3-+` `flip-+`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

34.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
5.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
40.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify487.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2015
2	708
1	268
0	107

prune916.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 20.7b

regimes387.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

794.0ms

8465×

body

valid