Details

sample35.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	191×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	13×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	5×	body	160	valid

simplify10.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 14.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

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:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(/ 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)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2500	828
3	5001	827

prune257.0ms

Filtered

93 candidates to 71 candidates (76.3%)

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: 13.7b

Counts

94 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	269	900
1	805	835
2	2267	823
3	5002	822

prune286.0ms

Filtered

97 candidates to 71 candidates (73.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	94	17	111

Merged error: 13.7b

Counts

111 → 17

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

14.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
15.0ms	(log (sqrt (exp (+ 1.0 (/ x (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)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
178.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	864
1	350	792
2	912	792
3	2173	792
4	5001	792

prune391.0ms

Filtered

86 candidates to 72 candidates (83.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	86	17	103

Merged error: 13.7b

Counts

103 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

17.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0ms	(log (sqrt (exp (+ 1.0 (/ x (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)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
177.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify109.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	210	699
1	535	644
2	1426	643
3	3668	636
4	5002	636

prune324.0ms

Filtered

76 candidates to 65 candidates (85.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	8	7	15
Picked	1	0	1
Done	1	0	1
Total	77	16	93

Merged error: 13.7b

Counts

93 → 16

regimes407.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample840.0ms

Algorithm

intervals

Results

217.0ms	6046×	body	80	valid
187.0ms	817×	body	2560	valid
107.0ms	602×	body	1280	valid
104.0ms	8000×	pre	80	true
43.0ms	310×	body	640	valid
16.0ms	153×	body	320	valid
5.0ms	72×	body	160	valid