Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	194×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
2.0ms	14×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite125.0ms

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:

16.0ms	(+ (* (* 4.0 p) p) (* x x))
27.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* (* 4.0 p) p) (* x x))
71.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune258.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite307.0ms

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:

27.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
201.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
70.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
66.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (58.0ms)

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

prune320.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
14×	`cbrt-prod`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`unpow-prod-down` `flip3-+` `sqrt-div` `cube-prod` `flip-+`
3×	`distribute-lft-out` `associate-/l*`
2×	`cube-div` `cbrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `div-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

99.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
71.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify124.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	318	1044
1	1169	1010
2	4563	1005
3	5001	1005

prune397.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite303.0ms

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:

27.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
198.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
71.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
66.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (60.0ms)

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

prune343.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.5b

regimes245.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample863.0ms

Algorithm

intervals

Results

209.0ms	6054×	body	80	valid
183.0ms	805×	body	2560	valid
108.0ms	622×	body	1280	valid
101.0ms	8000×	pre	80	true
42.0ms	298×	body	640	valid
13.0ms	130×	body	320	valid
6.0ms	91×	body	160	valid