Details

sample52.0ms

Algorithm

intervals

Results

22.0ms

265×

body

valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
23.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite51.0ms

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:

11.0ms	(- (* b c) (* a d))
38.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series220.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (* b c) (* a d))
165.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.7s

Counts

50 → 50

Iterations

Useful iterations: 3 (812.0ms)

Iter	Nodes	Cost
0	86	954
1	254	936
2	980	856
3	4329	850
done	5001	850

prune235.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.1b	(sqrt (+ (* c c) (* d d)))
26.1b	(sqrt (+ (* c c) (* d d)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`flip3--` `flip--`

Counts

4 → 266

Calls

4 calls:

36.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
25.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
129.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify818.0ms

Counts

278 → 278

Iterations

Useful iterations: done (808.0ms)

Iter	Nodes	Cost
0	307	11144
1	764	10034
2	3205	9469
done	5000	9101

prune914.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* b c) (* a d))
0.4b	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
23.1b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

834×	`times-frac`
380×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
144×	`sqrt-prod`
49×	`associate-/r/`
41×	`div-inv`
27×	`add-exp-log`
25×	`flip3--` `flip--` `associate-/l*`
18×	`associate-/r*`
17×	`add-cbrt-cube` `div-exp`
9×	`cbrt-undiv`
5×	`add-log-exp`
3×	`pow1` `associate-/l/`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 434

Calls

3 calls:

6.0ms	(- (* b c) (* a d))
35.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
25.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (* b c) (* a d))
138.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
66.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify995.0ms

Counts

443 → 443

Iterations

Useful iterations: done (977.0ms)

Iter	Nodes	Cost
0	622	18020
1	2243	13890
done	5001	13565

prune537.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.1b

localize26.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(cbrt (+ (* c c) (* d d)))
27.1b	(cbrt (+ (* c c) (* d d)))

rewrite41.0ms

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:

25.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
97.0ms	(cbrt (+ (* c c) (* d d)))
99.0ms	(cbrt (+ (* c c) (* d d)))

simplify430.0ms

Counts

97 → 97

Iterations

Useful iterations: done (428.0ms)

Iter	Nodes	Cost
0	135	1897
1	335	1785
2	1289	1635
done	5001	1627

prune495.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 20.1b

regimes381.0ms

Accuracy

3.7% (3.0b remaining)

Error of 25.8b against oracle of 22.8b and baseline of 25.9b

bsearch35.0ms

Steps

Iters	Range		Point
7	2.779174960643886e+83	1.7372164856765643e+85	1.0110714407946299e+85

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	23	40
done	23	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

753.0ms

8456×

body

valid