Details

sample50.0ms

Algorithm

intervals

Results

21.0ms

275×

body

valid

simplify63.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize25.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* b c) (* a d))
24.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

6.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series214.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (* b c) (* a d))
142.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5001
3	2806
2	837
1	254
0	86

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.2b

localize43.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(sqrt (+ (* c c) (* d d)))

rewrite62.0ms

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:

9.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* b c) (* a d))
170.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
52.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts

98 → 98

Iterations

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

prune520.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
1.1b	(- (* b c) (* a d))
24.3b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

21.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
6.0ms	(- (* b c) (* a d))
30.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ 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)))

simplify1.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
3	4845
2	1484
1	530
0	192

prune621.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

localize38.0ms

Local error

Found 4 expressions with local error:

15.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
32.3b	(cbrt (+ (* c c) (* d d)))
32.3b	(cbrt (+ (* c c) (* d d)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`cbrt-prod` `associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 85

Calls

4 calls:

27.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
103.0ms	(cbrt (+ (* c c) (* d d)))
105.0ms	(cbrt (+ (* c c) (* d d)))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	3010
2	905
1	327
0	135

prune581.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.4b

regimes322.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample886.0ms

Algorithm

intervals

Results

450.0ms

8432×

body

valid