Details

sample63.0ms

Algorithm

intervals

Results

12.0ms	194×	body	80	valid
11.0ms	19×	body	1280	valid
10.0ms	24×	body	2560	valid
6.0ms	256×	pre	80	true
4.0ms	14×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9

prune2.0ms

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)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`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×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
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 → 91

Calls

4 calls:

18.0ms	(+ (* (* 4.0 p) p) (* x x))
31.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
70.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* (* 4.0 p) p) (* x x))
54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
68.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify158.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune330.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

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)))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log-prod` `exp-prod` `sqrt-div` `log1p-expm1-u`
3×	`fma-def` `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 → 96

Calls

4 calls:

30.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
214.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
70.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
70.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	286	957
1	875	889
2	2480	876
3	5002	874

prune400.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite490.0ms

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×	`expm1-log1p-u` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `rem-log-exp` `exp-sum` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

217.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
217.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
160.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	163	930
1	392	856
2	1050	856
3	2648	856
4	5001	856

prune502.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
4.1b	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-pow`
32×	`sqrt-pow1`
28×	`exp-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`times-frac`
13×	`log-prod`
10×	`pow1`
6×	`add-exp-log` `sqrt-div`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `rem-log-exp` `associate-/r/`
1×	`exp-sum` `div-inv` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

213.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
68.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
115.0ms	(log (sqrt (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	276	1053
1	605	972
2	1553	959
3	3847	959
4	5001	959

prune621.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

regimes116.0ms

Accuracy

0% (0.3b 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	35	43
1	35	43

end0.0ms

sample880.0ms

Algorithm

intervals

Results

213.0ms	6054×	body	80	valid
184.0ms	805×	body	2560	valid
117.0ms	622×	body	1280	valid
103.0ms	8000×	pre	80	true
41.0ms	298×	body	640	valid
14.0ms	130×	body	320	valid
6.0ms	91×	body	160	valid