Details

sample38.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
5.0ms	25×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
3.0ms	21×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize11.0ms

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)))

rewrite131.0ms

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:

29.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
18.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms	(+ (* (* 4.0 p) p) (* x x))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

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

prune300.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize26.0ms

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)))

rewrite132.0ms

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:

72.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(/ x (fma (* 4.0 p) p (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(/ x (fma (* 4.0 p) p (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (54.0ms)

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

prune605.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize12.0ms

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)))

rewrite125.0ms

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:

17.0ms	(+ (* (* 4.0 p) p) (* x x))
73.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 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	866
1	1987	780
2	5002	742

prune325.0ms

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)))

rewrite120.0ms

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)))))
86.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
167.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
134.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
130.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.8b

regimes153.0ms

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

sample906.0ms

Algorithm

intervals

Results

207.0ms	6023×	body	80	valid
187.0ms	814×	body	2560	valid
113.0ms	639×	body	1280	valid
107.0ms	8000×	pre	80	true
42.0ms	305×	body	640	valid
20.0ms	143×	body	320	valid
5.0ms	76×	body	160	valid