Details

sample40.0ms

Algorithm

intervals

Results

18.0ms

271×

body

valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	72
5	72
4	66
3	48
2	36
1	19
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
25.3b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite53.0ms

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:

12.0ms	(+ (* c c) (* d d))
11.0ms	(- (* b c) (* a d))
27.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* c c) (* d d))
71.0ms	(- (* b c) (* a d))
162.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1712
1	315
0	99

prune368.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite78.0ms

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))
40.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
11.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b c) (* a d))
134.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
67.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1128
1	308
0	118

prune635.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.0b

localize50.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `flip-+`
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` `flip3--` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `flip--`

Counts

4 → 77

Calls

4 calls:

39.0ms	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
17.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (* b c) (* a d)) (* (sqrt (sqrt (+ (* c c) (* d d)))) (sqrt (sqrt (+ (* c c) (* d d))))))
56.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	3024
2	956
1	314
0	110

prune664.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
25.1b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite76.0ms

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:

10.0ms	(+ (* c c) (* d d))
12.0ms	(- (* b c) (* a d))
22.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
25.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* c c) (* d d))
64.0ms	(- (* b c) (* a d))
173.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
64.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify1.7s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	3521
1	586
0	205

prune609.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.0b

regimes324.0ms

Accuracy

0% (3.1b remaining)

Error of 26.0b against oracle of 22.9b and baseline of 26.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample871.0ms

Algorithm

intervals

Results

471.0ms

8499×

body

valid