Details

sample128.0ms

Algorithm

intervals

Results

69.0ms	304×	body	80	valid
22.0ms	97×	body	80	nan

simplify919.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
4	2008
3	596
2	95
1	38
0	17

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize49.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) d)
3.8b	(/ (* M D) d)
5.7b	(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
12.3b	(/ (/ (/ (* M D) d) 2) (/ l h))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

985×	`times-frac`
388×	`add-sqr-sqrt`
387×	`*-un-lft-identity` `add-cube-cbrt`
85×	`div-inv`
46×	`add-cbrt-cube` `add-exp-log`
27×	`associate-/l*`
26×	`cbrt-undiv` `div-exp`
19×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`

Counts

4 → 460

Calls

4 calls:

9.0ms	(/ (* M D) d)
9.0ms	(/ (* M D) d)
6.0ms	(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
34.0ms	(/ (/ (/ (* M D) d) 2) (/ l h))

series380.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) d)
36.0ms	(/ (* M D) d)
198.0ms	(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
118.0ms	(/ (/ (/ (* M D) d) 2) (/ l h))

simplify1.3s

Counts

472 → 472

Iterations

Iter	Nodes
done	2000
1	2000
0	864

prune4.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize58.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) d)
3.8b	(/ (* M D) d)
5.7b	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
8.8b	(/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

3244×	`times-frac`
1242×	`add-sqr-sqrt`
1241×	`*-un-lft-identity` `add-cube-cbrt`
486×	`sqrt-prod`
423×	`cbrt-prod`
211×	`div-inv`
48×	`associate-/l*`
46×	`add-exp-log`
42×	`add-cbrt-cube`
28×	`associate-/r*`
26×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`

Counts

4 → 1177

Calls

4 calls:

16.0ms	(/ (* M D) d)
9.0ms	(/ (* M D) d)
6.0ms	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
20.0ms	(/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))

series2.3s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* M D) d)
34.0ms	(/ (* M D) d)
1.6s	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
637.0ms	(/ (/ (/ (* M D) d) (sqrt 2)) (/ (cbrt l) h))

simplify2.6s

Counts

1189 → 1189

Iterations

Iter	Nodes
done	2001
1	2001
0	1644

prune14.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize126.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) d)
3.8b	(/ (* M D) d)
5.7b	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h)))) (/ (/ (* M D) d) 2))))
6.9b	(/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

2749×	`times-frac`
1046×	`add-sqr-sqrt`
1045×	`*-un-lft-identity` `add-cube-cbrt`
885×	`sqrt-prod`
211×	`div-inv`
74×	`add-exp-log`
69×	`associate-/l*`
48×	`div-exp`
46×	`add-cbrt-cube`
26×	`cbrt-undiv`
19×	`associate-/r*`
6×	`prod-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`

Counts

4 → 1056

Calls

4 calls:

9.0ms	(/ (* M D) d)
9.0ms	(/ (* M D) d)
10.0ms	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h)))) (/ (/ (* M D) d) 2))))
47.0ms	(/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h))

series2.1s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* M D) d)
38.0ms	(/ (* M D) d)
1.7s	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h)))) (/ (/ (* M D) d) 2))))
330.0ms	(/ (/ (/ (* M D) d) (sqrt (sqrt 2))) (/ 1 h))

simplify2.7s

Counts

1068 → 1068

Iterations

Iter	Nodes
done	2001
1	2001
0	1385

prune12.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

localize143.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (/ 1 h) (/ (cbrt (/ (* M D) d)) (sqrt (sqrt 2))))))) (/ (/ (* M D) d) 2))))
20.7b	(cbrt (/ (* M D) d))
20.7b	(cbrt (/ (* M D) d))
20.7b	(cbrt (/ (* M D) d))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 75

Calls

4 calls:

6.0ms	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (/ 1 h) (/ (cbrt (/ (* M D) d)) (sqrt (sqrt 2))))))) (/ (/ (* M D) d) 2))))
3.0ms	(cbrt (/ (* M D) d))
3.0ms	(cbrt (/ (* M D) d))
3.0ms	(cbrt (/ (* M D) d))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt (- 1 (* (* (/ (/ 1 (sqrt 2)) (* (cbrt l) (cbrt l))) (* (/ (/ 1 (sqrt (sqrt 2))) (cbrt l)) (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (/ 1 h) (/ (cbrt (/ (* M D) d)) (sqrt (sqrt 2))))))) (/ (/ (* M D) d) 2))))
110.0ms	(cbrt (/ (* M D) d))
131.0ms	(cbrt (/ (* M D) d))
148.0ms	(cbrt (/ (* M D) d))

simplify2.5s

Counts

87 → 87

Iterations

Iter	Nodes
done	2001
3	2001
2	787
1	241
0	124

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 7.1b

regimes1.5s

Accuracy

0% (1.1b remaining)

Error of 8.1b against oracle of 7.1b and baseline of 8.1b

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.9s	9260×	body	80	valid
624.0ms	2989×	body	80	nan