Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7
done	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
25.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite43.0ms

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

Counts

3 → 55

Calls

3 calls:

8.0ms	(+ (* c c) (* d d))
8.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
45.0ms	(- (* b c) (* a d))
92.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491
done	5002	491

prune169.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 25.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite55.0ms

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

Counts

4 → 86

Calls

4 calls:

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

series238.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b c) (* a d))
120.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify97.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845
done	5001	845

prune270.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
25.5b	(/ (- (* b c) (* a d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
40.0ms	(/ (- (* b c) (* a d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
93.0ms	(/ (- (* b c) (* a d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
38.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify103.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	331	792
1	1162	699
2	4016	680
3	5001	680
done	5001	680

prune236.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 22.7b

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ b (/ (+ (* c c) (* d d)) c))
4.1b	(/ a (/ (+ (* c c) (* d d)) d))
17.1b	(/ (+ (* c c) (* d d)) d)
17.3b	(/ (+ (* c c) (* d d)) c)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
104×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv` `associate-/l*`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 198

Calls

4 calls:

14.0ms	(/ b (/ (+ (* c c) (* d d)) c))
17.0ms	(/ a (/ (+ (* c c) (* d d)) d))
24.0ms	(/ (+ (* c c) (* d d)) d)
25.0ms	(/ (+ (* c c) (* d d)) c)

series193.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ b (/ (+ (* c c) (* d d)) c))
48.0ms	(/ a (/ (+ (* c c) (* d d)) d))
43.0ms	(/ (+ (* c c) (* d d)) d)
51.0ms	(/ (+ (* c c) (* d d)) c)

simplify83.0ms

Counts

210 → 210

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	717	2042
1	3290	1930
2	5001	1930
done	5001	1930

prune550.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

regimes173.0ms

Accuracy

87.4% (1.0b remaining)

Error of 8.6b against oracle of 7.5b and baseline of 15.6b

bsearch93.0ms

Steps

Iters	Range		Point
10	7.396278648736192e+140	2.3200696560285643e+156	8.000358861136643e+153
9	-9.407223570539366e+155	-8.928275251414201e+148	-1.3512147215494832e+154

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20
done	34	20

end0.0ms

sample584.0ms

Algorithm

intervals

Results

288.0ms

8466×

body

valid