Details

sample55.0ms

Algorithm

intervals

Results

11.0ms	222×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
2.0ms	7×	body	2560	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	640	valid
0.0ms	1×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 7.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms	(+ (* (* 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)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune187.0ms

Filtered

91 candidates to 67 candidates (26.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 7.2b

Counts

92 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.3b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

13.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms	(log (exp (+ 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)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify111.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506

prune159.0ms

Filtered

70 candidates to 56 candidates (20.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	11	79

Merged error: 7.2b

Counts

79 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.9b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	384	1288
1	1307	1207
2	5001	1169

prune281.0ms

Filtered

106 candidates to 77 candidates (27.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	107	10	117

Merged error: 7.2b

Counts

117 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.9b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
19.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

9.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	384	1288
1	1307	1207
2	5001	1169

prune285.0ms

Filtered

106 candidates to 77 candidates (27.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	106	10	116

Merged error: 7.2b

Counts

116 → 10

regimes361.0ms

Accuracy

0% (0.2b remaining)

Error of 6.5b against oracle of 6.4b and baseline of 6.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample939.0ms

Algorithm

intervals

Results

347.0ms	7043×	body	80	valid
133.0ms	8000×	pre	80	true
93.0ms	311×	body	2560	valid
70.0ms	286×	body	1280	valid
35.0ms	182×	body	640	valid
19.0ms	125×	body	320	valid
5.0ms	53×	body	160	valid

Details

sample55.0ms

simplify14.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series45.0ms

simplify152.0ms

prune187.0ms

localize15.0ms

rewrite43.0ms

series56.0ms

simplify111.0ms

prune159.0ms

localize15.0ms

rewrite26.0ms

series60.0ms

simplify49.0ms

prune281.0ms

localize18.0ms

rewrite24.0ms

series61.0ms

simplify51.0ms

prune285.0ms

regimes361.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample939.0ms

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