Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
6.0ms	26×	body	2560	valid
4.0ms	23×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify14.0ms

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: 12.4b

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	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

57.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
19.0ms	(+ (* (* 4.0 p) p) (* x x))
58.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
35.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify98.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	260	581
1	922	542
2	3335	537
3	5001	533

prune250.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize22.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 4 (81.0ms)

Iter	Nodes	Cost
0	106	548
1	323	528
2	963	528
3	2523	528
4	5002	524

prune475.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.8b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 136

Calls

4 calls:

127.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	306	1424
1	1152	1313
2	5002	1274

prune427.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
11.2b	(+ 1.0 (/ x (* (pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3) (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 103

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
76.0ms	(+ 1.0 (/ x (* (pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3) (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
79.0ms	(+ 1.0 (/ x (* (pow (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3) (sqrt (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	454	1275
1	1491	1168
2	5002	1151

prune424.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

regimes291.0ms

Accuracy

0% (0.8b remaining)

Error of 13.7b against oracle of 12.8b and baseline of 13.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms

sample870.0ms

Algorithm

intervals

Results

209.0ms	6035×	body	80	valid
175.0ms	812×	body	2560	valid
109.0ms	8000×	pre	80	true
104.0ms	616×	body	1280	valid
40.0ms	300×	body	640	valid
16.0ms	153×	body	320	valid
6.0ms	84×	body	160	valid