Details

sample12.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
3.0ms	(sqrt (+ (* x x) (* y y)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
37.0ms	(sqrt (+ (* x x) (* y y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	125	177
1	530	163
2	1540	163
3	5001	162

prune68.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.8b	(exp (log (sqrt (+ (* x x) (* y y)))))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-exp-log`

Counts

3 → 48

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
5.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
3.0ms	(sqrt (+ (* x x) (* y y)))

series98.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
37.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
34.0ms	(sqrt (+ (* x x) (* y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	172	330
1	601	313
2	1676	304
3	5001	296

prune117.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod` `sqrt-div`
5×	`add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
3×	`unpow-prod-down` `rem-sqrt-square` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

4.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
34.0ms	(sqrt (+ (* x x) (* y y)))
34.0ms	(sqrt (+ (* x x) (* y y)))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	189	925
1	499	852
2	1541	846
3	5002	842

prune263.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))
29.5b	(log (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down`
8×	`pow1`
7×	`pow-unpow`
6×	`add-exp-log` `sqrt-prod`
4×	`cbrt-prod` `sqrt-div` `pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `flip3-+` `flip-+`
2×	`pow-to-exp` `rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `log-pow` `sqr-pow`
1×	`pow-pow` `rem-log-exp`

Counts

4 → 71

Calls

4 calls:

4.0ms	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(log (+ (* x x) (* y y)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

503.0ms	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
34.0ms	(sqrt (+ (* x x) (* y y)))
34.0ms	(sqrt (+ (* x x) (* y y)))
50.0ms	(log (+ (* x x) (* y y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	293	1150
1	702	1101
2	2167	1097
3	5001	1093

prune318.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

regimes243.0ms

Accuracy

57.1% (10.2b remaining)

Error of 18.2b against oracle of 8.0b and baseline of 31.7b

bsearch22.0ms

Steps

Iters	Range		Point
5	6.409367159269928e+131	1.4522094872280968e+132	9.634966723363643e+131
2	-2.319338119088684e+59	-1.9710212454209794e+59	-2.2710920961423764e+59

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

sample302.0ms

Algorithm

intervals

Results

176.0ms

8000×

body

valid