Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	186×	body	80	valid
6.0ms	25×	body	2560	valid
4.0ms	19×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	21×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize12.0ms

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))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite136.0ms

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:

30.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
18.0ms	(+ (* (* 4.0 p) p) (* x x))
57.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
35.0ms	(+ (* (* 4.0 p) p) (* x x))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify153.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (144.0ms)

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

prune312.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.9b	(/ x (fma (* 4.0 p) p (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
78×	`add-cube-cbrt`
72×	`prod-diff`
65×	`times-frac`
34×	`sqrt-prod`
10×	`sqrt-div`
6×	`pow1` `add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r` `associate-/l` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

75.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(/ x (fma (* 4.0 p) p (* x x)))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(/ x (fma (* 4.0 p) p (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	682	4617
1	2256	3256
2	5001	2931

prune611.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

18.0ms	(+ (* (* 4.0 p) p) (* x x))
76.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* (* 4.0 p) p) (* x x))
60.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
81.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	405	867
1	1999	779
2	5001	742

prune318.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
6.9b	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1/3`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

5.0ms	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
89.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
18.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
184.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
140.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
142.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	406	1075
1	1472	979
2	5002	968

prune378.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.8b

regimes161.0ms

Accuracy

0% (1.6b remaining)

Error of 14.8b against oracle of 13.2b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample916.0ms

Algorithm

intervals

Results

220.0ms	6023×	body	80	valid
192.0ms	814×	body	2560	valid
123.0ms	639×	body	1280	valid
104.0ms	8000×	pre	80	true
44.0ms	305×	body	640	valid
16.0ms	143×	body	320	valid
5.0ms	76×	body	160	valid