Details

sample57.0ms

Algorithm

intervals

Results

39.0ms

275×

body

valid

simplify66.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	70
5	70
4	66
3	48
2	36
1	19
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
24.7b	(/ (- (* 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))
29.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* c c) (* d d))
59.0ms	(- (* b c) (* a d))
113.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
3	4155
2	1093
1	299
0	99

prune609.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.8b	(sqrt (+ (* c c) (* d d)))
27.8b	(sqrt (+ (* c c) (* d d)))

rewrite41.0ms

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:

6.0ms	(- (* b c) (* a d))
18.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b c) (* a d))
145.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
60.0ms	(sqrt (+ (* c c) (* d d)))

simplify772.0ms

Counts

98 → 98

Iterations

Iter	Nodes
3	2518
2	887
1	307
0	118

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
24.4b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite62.0ms

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))
6.0ms	(- (* b c) (* a d))
20.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
28.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* c c) (* d d))
49.0ms	(- (* b c) (* a d))
170.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
74.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify7.8s

Counts

150 → 150

Iterations

Iter	Nodes
3	6745
2	1683
1	560
0	205

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.2b

localize31.0ms

Local error

Found 4 expressions with local error:

12.0b	(/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (cbrt (+ (* c c) (* d d)))))
28.7b	(cbrt (+ (* c c) (* d d)))
28.7b	(cbrt (+ (* c c) (* d d)))
28.7b	(cbrt (+ (* c c) (* d d)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
33×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`cbrt-prod`
24×	`associate-/r*`
22×	`cbrt-div`
16×	`add-exp-log`
11×	`flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`frac-times` `pow1` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

32.0ms	(/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (cbrt (+ (* c c) (* d d)))))
3.0ms	(cbrt (+ (* c c) (* d d)))
3.0ms	(cbrt (+ (* c c) (* d d)))
3.0ms	(cbrt (+ (* c c) (* d d)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (cbrt (+ (* c c) (* d d)))))
96.0ms	(cbrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
2	2623
1	577
0	200

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.2b

regimes311.0ms

Accuracy

0% (2.4b remaining)

Error of 25.3b against oracle of 22.8b and baseline of 25.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	16
1	16
0	13

end0.0ms

sample994.0ms

Algorithm

intervals

Results

762.0ms

8454×

body

valid