Details

sample53.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
10.0ms	25×	body	2560	valid
5.0ms	256×	pre	80	true
3.0ms	10×	body	1280	valid
3.0ms	10×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

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: 12.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

25.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series411.0ms

Counts

3 → 9

Calls

3 calls:

279.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))

simplify119.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	206	431
1	565	404
2	1561	403
3	4083	403
4	5001	403

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.4b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`pow1` `add-log-exp`
5×	`times-frac`
4×	`sqrt-div`
3×	`flip3-+` `associate-/r*` `flip-+` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r/`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

25.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	269	680
1	1092	624
2	4346	614
3	5002	614

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize21.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (exp (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.4b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`log-pow`
7×	`pow1` `exp-prod` `sqrt-prod`
5×	`log-prod` `times-frac`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `exp-sum` `associate-/r/`
1×	`sub-neg` `log-div` `frac-2neg` `exp-diff` `rem-log-exp` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 75

Calls

4 calls:

94.0ms	(log (exp (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(log (exp (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify108.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	261	691
1	1032	621
2	4134	619
3	5001	619

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

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)))))
7.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* 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)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `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×	`frac-times`
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 → 125

Calls

4 calls:

53.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

simplify51.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	290	1356
1	1084	1258
2	5001	1216

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

regimes146.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	29
1	31	29

end0.0ms

sample1.4s

Algorithm

intervals

Results

456.0ms	6123×	body	80	valid
276.0ms	717×	body	2560	valid
189.0ms	594×	body	1280	valid
145.0ms	8000×	pre	80	true
82.0ms	322×	body	640	valid
27.0ms	58×	body	5120	valid
25.0ms	125×	body	320	valid
8.0ms	61×	body	160	valid