Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

275×

body

valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* b c) (* a d))
22.3b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.0s

Counts

50 → 50

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	88	954
1	250	936
2	811	854
3	2609	850
done	5001	849

prune141.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
12.0b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

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:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
116.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify983.0ms

Counts

98 → 98

Iterations

Useful iterations: done (981.0ms)

Iter	Nodes	Cost
0	120	1814
1	304	1682
2	854	1574
3	2501	1558
done	5000	1557

prune277.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* d a))
12.1b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* d a)))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* c c) (* d d)))

rewrite21.0ms

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

Counts

4 → 85

Calls

4 calls:

2.0ms	(- (* b c) (* d a))
10.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* d a)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* d a))
77.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* d a)))
35.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.4s

Counts

97 → 97

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	113	1782
1	263	1664
2	702	1562
3	1803	1548
4	4588	1547
done	5000	1547

prune276.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
12.1b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* c c) (* d d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
27.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b c) (* a d))
108.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
37.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.1s

Counts

107 → 107

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	147	1896
1	377	1651
2	1057	1497
3	3862	1481
done	5001	1481

prune279.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.9b

regimes177.0ms

Accuracy

0% (2.2b remaining)

Error of 25.9b against oracle of 23.8b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	20	27
done	20	27

end0.0ms

sample502.0ms

Algorithm

intervals

Results

294.0ms

8478×

body

valid