Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	190×	body	80	valid
11.0ms	24×	body	2560	valid
9.0ms	22×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	11×	body	320	valid
2.0ms	5×	body	640	valid
1.0ms	4×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

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:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* (* 4.0 p) p) (* x x))
64.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
84.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify145.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (136.0ms)

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

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

16.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
32.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
56.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	384	1256
1	1710	1134
2	5001	1063

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b	(+ 1.0 (expm1 (log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
4.4b	(log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

33.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (expm1 (log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.0ms	(log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
177.0ms	(+ 1.0 (expm1 (log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
121.0ms	(log1p (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	405	946
1	1731	837
2	5001	791

prune362.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.3b	(fma (pow x 3) (/ 1 (pow (sqrt (+ (* (* 4.0 p) p) (* x x))) 3)) (pow 1.0 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
0.0ms	(fma (pow x 3) (/ 1 (pow (sqrt (+ (* (* 4.0 p) p) (* x x))) 3)) (pow 1.0 3))

series264.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
89.0ms	(fma (pow x 3) (/ 1 (pow (sqrt (+ (* (* 4.0 p) p) (* x x))) 3)) (pow 1.0 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	136	540
1	423	512
2	1726	512
3	5001	507

prune372.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.0b

regimes94.0ms

Accuracy

0% (8.0b remaining)

Error of 13.8b against oracle of 5.8b and baseline of 13.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

552.0ms	5995×	body	80	valid
373.0ms	819×	body	2560	valid
230.0ms	614×	body	1280	valid
164.0ms	8000×	pre	80	true
98.0ms	326×	body	640	valid
39.0ms	166×	body	320	valid
13.0ms	80×	body	160	valid