Details

sample343.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
8.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
3.0ms	15×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

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: 13.1b

Counts

2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
38.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2486	828
3	5001	827

prune213.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	79	14	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	14	94

Merged error: 12.9b

Counts

94 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.4b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod` `add-log-exp`
5×	`distribute-lft-out`
4×	`unpow-prod-down` `flip3-+` `sqrt-div` `cube-prod` `flip-+`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `sum-cubes` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 70

Calls

4 calls:

36.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
9.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	296	693
1	1364	633
2	5001	630

prune257.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	82	14	96

Merged error: 12.9b

Counts

96 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.4b	(/ (+ (* (* 4.0 p) p) (* x x)) (* x x))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod` `add-log-exp`
5×	`distribute-lft-out`
4×	`unpow-prod-down` `flip3-+` `sqrt-div` `cube-prod` `flip-+`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/l/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `sum-log` `sum-cubes` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

37.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
9.0ms	(/ (+ (* (* 4.0 p) p) (* x x)) (* x x))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
9.0ms	(/ (+ (* (* 4.0 p) p) (* x x)) (* x x))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	312	706
1	1403	646
2	5002	646

prune273.0ms

Filtered

66 candidates to 82 candidates (-24.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	82	14	96

Merged error: 12.9b

Counts

96 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
32.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	234	637
1	607	590
2	1618	589
3	4163	589
4	5001	589

prune143.0ms

Filtered

60 candidates to 68 candidates (-13.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	3	9	12
Picked	1	0	1
Done	1	0	1
Total	69	13	82

Merged error: 12.9b

Counts

82 → 13

regimes397.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	29
1	31	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

308.0ms	6017×	body	80	valid
244.0ms	785×	body	2560	valid
166.0ms	632×	body	1280	valid
144.0ms	8000×	pre	80	true
64.0ms	317×	body	640	valid
24.0ms	161×	body	320	valid
9.0ms	88×	body	160	valid

Details

sample343.0ms

simplify8.0ms

prune3.0ms

localize35.0ms

rewrite40.0ms

series72.0ms

simplify76.0ms

prune213.0ms

localize21.0ms

rewrite59.0ms

series40.0ms

simplify45.0ms

prune257.0ms

localize20.0ms

rewrite58.0ms

series39.0ms

simplify44.0ms

prune273.0ms

localize14.0ms

rewrite34.0ms

series105.0ms

simplify122.0ms

prune143.0ms

regimes397.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

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