Details

analyze790.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

10.0ms	32×	body	2560	valid
10.0ms	190×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	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: 13.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(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)))

simplify113.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	431
1	565	404
2	1561	403
3	4083	403
4	5001	403

prune110.0ms

Filtered

43 candidates to 49 candidates (-14.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 13.2b

Counts

50 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.9b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify116.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	269	680
1	1092	624
2	4346	614
3	5003	614

prune236.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 13.2b

Counts

87 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b	(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(- 1.0 (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1` `log-prod` `exp-sum`
6×	`exp-prod` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `log-pow` `flip-+`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

7.0ms	(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
19.0ms	(- 1.0 (/ x (exp (log (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)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(- 1.0 (/ x (exp (log (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)))

simplify110.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 4 (101.0ms)

Iter	Nodes	Cost
0	222	721
1	510	686
2	1290	666
3	3279	658
4	5002	657

prune302.0ms

Filtered

67 candidates to 81 candidates (-20.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 13.2b

Counts

88 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune427.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	69	12	81

Merged error: 13.2b

Counts

81 → 12

regimes310.0ms

Accuracy

82.2% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 15.0b

bsearch37.0ms

Steps

Iters	Range		Point
7	-7.383907664962524e-119	-3.492945761894721e-120	-1.727158006251015e-119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	63
1	49	63

end0.0ms

analyze766.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

318.0ms	6001×	body	80	valid
262.0ms	802×	body	2560	valid
162.0ms	625×	body	1280	valid
142.0ms	8000×	pre	80	true
68.0ms	331×	body	640	valid
26.0ms	167×	body	320	valid
9.0ms	74×	body	160	valid

Details

analyze790.0ms

sample40.0ms

simplify8.0ms

prune3.0ms

localize11.0ms

rewrite32.0ms

series50.0ms

simplify113.0ms

prune110.0ms

localize21.0ms

rewrite32.0ms

series36.0ms

simplify116.0ms

prune236.0ms

localize24.0ms

rewrite38.0ms

series35.0ms

simplify110.0ms

prune302.0ms

localize34.0ms

rewrite22.0ms

series32.0ms

simplify86.0ms

prune427.0ms

regimes310.0ms

bsearch37.0ms

simplify2.0ms

end0.0ms

analyze766.0ms

sample1.1s

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