Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

276×

body

valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
25.7b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite41.0ms

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`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 55

Calls

3 calls:

6.0ms	(+ (* c c) (* d d))
6.0ms	(- (* b c) (* a d))
28.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* c c) (* d d))
61.0ms	(- (* b c) (* a d))
131.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5113
3	4064
2	1053
1	300
0	99

prune451.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 25.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite63.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

11.0ms	(- (* b c) (* a d))
27.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b c) (* a d))
160.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
68.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5012
3	2587
2	896
1	308
0	118

prune622.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.2b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite81.0ms

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×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3-+` `flip3--` `associate-l` `flip-+` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

6.0ms	(- (* b c) (* a d))
54.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
12.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b c) (* a d))
166.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
47.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
3	3349
2	1094
1	393
0	145

prune559.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
0.7b	(- (* b c) (* a d))
25.2b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 138

Calls

4 calls:

6.0ms	(+ (* c c) (* d d))
20.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
6.0ms	(- (* b c) (* a d))
29.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* c c) (* d d))
143.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
45.0ms	(- (* b c) (* a d))
66.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify1.0s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	1655
1	568
0	205

prune625.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.0b

regimes285.0ms

Accuracy

-1.8% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch45.0ms

Steps

Iters	Range		Point
9	2.1675332614166088e+58	1.841919235217342e+66	1.9376700173410365e+62

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

810.0ms

8474×

body

valid