Details

sample38.0ms

Algorithm

intervals

Results

20.0ms

273×

body

valid

simplify10.0ms

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: 26.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.5b	(+ (* a c) (* b d))
25.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite67.0ms

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:

11.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))
47.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* c c) (* d d))
42.0ms	(+ (* a c) (* b d))
114.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify3.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
3	3905
2	997
1	279
0	96

prune455.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.2b

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* a c) (* b d))
16.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite54.0ms

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:

8.0ms	(+ (* a c) (* b d))
26.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* a c) (* b d))
191.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
69.0ms	(sqrt (+ (* c c) (* d d)))
72.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.4s

Counts

96 → 96

Iterations

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

prune675.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.8b

localize37.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* a c) (* b d))
16.4b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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))
23.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
11.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* a c) (* b d))
85.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
52.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
4	4986
3	1893
2	738
1	268
0	112

prune632.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

localize33.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* a c) (* b d))
16.4b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite106.0ms

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:

12.0ms	(+ (* a c) (* b d))
64.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
13.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* a c) (* b d))
159.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
62.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
3	3647
2	1212
1	401
0	143

prune582.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

regimes425.0ms

Accuracy

-3.4% (3.1b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.6b

bsearch29.0ms

Steps

Iters	Range		Point
5	-2.2871888563215003e+52	-5.952772209436251e+51	-1.1491009642806413e+52

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample870.0ms

Algorithm

intervals

Results

593.0ms

8459×

body

valid