Details

sample83.0ms

Algorithm

intervals

Results

26.0ms	197×	body	80	valid
17.0ms	22×	body	2560	valid
11.0ms	20×	body	1280	valid
7.0ms	256×	pre	80	true
3.0ms	8×	body	640	valid
2.0ms	7×	body	160	valid
0.0ms	2×	body	320	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize11.0ms

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))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`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×	`flip3-+` `sqrt-div` `flip-+`
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 → 79

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(/ 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)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* (* 4.0 p) p) (* x x))
54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify141.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune252.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
1.6b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt` `exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`sqrt-prod` `distribute-lft-out`
2×	`flip3-+` `sqrt-div` `exp-sum` `sum-log` `flip-+` `rem-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 58

Calls

4 calls:

95.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
96.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
81.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506

prune262.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
1.6b	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
18×	`log-pow`
17×	`exp-prod`
14×	`cbrt-prod` `add-sqr-sqrt`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-unpow` `log-prod` `flip3-+` `sqrt-prod` `flip-+`
2×	`cube-div` `cube-mult` `sqrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `sum-log` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

47.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
195.0ms	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
76.0ms	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	307	857
1	1117	790
2	5001	785

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
4.6b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

72.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
13.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
49.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	352	1043
1	1550	965
2	5001	964

prune420.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

regimes178.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	29
1	33	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

557.0ms	5986×	body	80	valid
409.0ms	882×	body	2560	valid
242.0ms	625×	body	1280	valid
162.0ms	8000×	pre	80	true
89.0ms	288×	body	640	valid
34.0ms	144×	body	320	valid
13.0ms	75×	body	160	valid