Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	32×	body	2560	valid
9.0ms	194×	body	80	valid
5.0ms	18×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 11.7b

localize13.0ms

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	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
29.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
50.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
66.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	297	951
1	884	898
2	2732	885
3	5001	883

prune300.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize17.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 86

Calls

4 calls:

16.0ms	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	249	953
1	715	923
2	2539	912
3	5001	909

prune419.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.6b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

31.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	359	1348
1	1263	1258
2	5001	1226

prune430.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
9.1b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

80.0ms	(* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
73.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (* x (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	477	1294
1	2211	1146
2	5001	1081

prune392.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.6b

regimes161.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	26
1	23	26

end0.0ms

sample874.0ms

Algorithm

intervals

Results

215.0ms	6060×	body	80	valid
187.0ms	827×	body	2560	valid
107.0ms	595×	body	1280	valid
98.0ms	8000×	pre	80	true
37.0ms	276×	body	640	valid
15.0ms	151×	body	320	valid
6.0ms	91×	body	160	valid