Details

sample53.0ms

Algorithm

intervals

Results

29.0ms

273×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
27.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

13.0ms	(+ (* c c) (* d d))
24.0ms	(+ (* a c) (* b d))
51.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* c c) (* d d))
54.0ms	(+ (* a c) (* b d))
139.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.3s

Counts

62 → 62

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	98	1090
1	297	1067
2	1661	953
done	5001	951

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
16.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
65.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
14.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* a c) (* b d))
195.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
67.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

96 → 96

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	116	1780
1	280	1649
2	1127	1543
done	5001	1541

prune726.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
16.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

19.0ms	(+ (* a c) (* b d))
60.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
15.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* a c) (* b d))
190.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
75.0ms	(sqrt (+ (* c c) (* d d)))
60.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

96 → 96

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	116	1780
1	280	1649
2	1127	1543
done	5001	1541

prune839.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.7b	(+ (* a c) (* b d))
26.9b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

14.0ms	(+ (* c c) (* d d))
45.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
14.0ms	(+ (* a c) (* b d))
65.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* c c) (* d d))
245.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
61.0ms	(+ (* a c) (* b d))
104.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify2.9s

Counts

149 → 149

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	206	3676
1	592	3422
2	4086	3218
done	5001	3214

prune677.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.5b

regimes441.0ms

Accuracy

-6.3% (3.1b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.3b

bsearch37.0ms

Steps

Iters	Range		Point
6	2.431590957525676e+49	1.8206035662555355e+50	1.0347324465362668e+50

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	21	39
done	21	39

end0.0ms

sample1.2s

Algorithm

intervals

Results

731.0ms

8471×

body

valid