Details

sample23.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
2.0ms	78×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 18.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
17.3b	(sqrt (+ (* x x) 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)
4.0ms	(sqrt (+ (* x x) y))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (* x x) y)
5.0ms	(sqrt (+ (* x x) y))

simplify46.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	139	151
1	485	141
2	1555	139
3	5002	138

prune44.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* x x) y)))
0.3b	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
18.1b	(cbrt (+ (* x x) y))
18.1b	(cbrt (+ (* x x) y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ (* x x) y)))
8.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
3.0ms	(cbrt (+ (* x x) y))
4.0ms	(cbrt (+ (* x x) y))

series78.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (cbrt (+ (* x x) y)))
28.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
16.0ms	(cbrt (+ (* x x) y))
17.0ms	(cbrt (+ (* x x) y))

simplify85.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	280	777
1	890	734
2	3434	706
3	5001	673

prune95.0ms

Filtered

72 candidates to 86 candidates (-19.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* -1/2 (/ y x))
0.0b	(- (* -1/2 (/ y x)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`

Counts

2 → 44

Calls

2 calls:

6.0ms	(* -1/2 (/ y x))
5.0ms	(- (* -1/2 (/ y x)) x)

series8.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* -1/2 (/ y x))
5.0ms	(- (* -1/2 (/ y x)) x)

simplify98.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	219	205
1	893	190
2	4202	189
3	5003	189

prune45.0ms

Filtered

34 candidates to 50 candidates (-47.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	50	4	54

Merged error: 0b

Counts

54 → 4

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

3.0ms	(+ x (* 1/2 (/ y x)))
6.0ms	(* 1/2 (/ y x))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ x (* 1/2 (/ y x)))
3.0ms	(* 1/2 (/ y x))

simplify98.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	223	199
1	960	186
2	4224	186
3	5001	186

prune42.0ms

Filtered

34 candidates to 49 candidates (-44.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	49	4	53

Merged error: 0b

Counts

53 → 4

regimes274.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 20.6b

bsearch22.0ms

Steps

Iters	Range		Point
6	1.8963249639503215e+100	2.41088961454771e+101	2.3710978095870002e+101
9	-2.2956361861733443e+156	-1.070067130940524e+149	-1.3507860660902314e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	9
1	22	9

end0.0ms

sample504.0ms

Algorithm

intervals

Results

190.0ms	8000×	body	80	valid
62.0ms	2726×	body	80	nan

Details

sample23.0ms

simplify3.0ms

prune2.0ms

localize4.0ms

rewrite7.0ms

series9.0ms

simplify46.0ms

prune44.0ms

localize8.0ms

rewrite21.0ms

series78.0ms

simplify85.0ms

prune95.0ms

localize5.0ms

rewrite12.0ms

series8.0ms

simplify98.0ms

prune45.0ms

localize4.0ms

rewrite10.0ms

series7.0ms

simplify98.0ms

prune42.0ms

regimes274.0ms

bsearch22.0ms

simplify1.0ms

end0.0ms

sample504.0ms

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