Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
6.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

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: 15.1b

localize16.0ms

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)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite80.0ms

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:

29.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(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

prune309.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
28.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
264.0ms	(log (exp (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)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	307	1011
1	849	934
2	2470	921
3	5002	919

prune405.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
102.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	286	956
1	875	889
2	2480	876
3	5002	874

prune404.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (/ x (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)))

simplify111.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 4 (99.0ms)

Iter	Nodes	Cost
0	180	588
1	522	546
2	1457	544
3	3954	542
4	5001	526

prune450.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.8b

regimes537.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	27
1	33	27

end0.0ms

sample929.0ms

Algorithm

intervals

Results

239.0ms	6019×	body	80	valid
198.0ms	791×	body	2560	valid
130.0ms	635×	body	1280	valid
123.0ms	8000×	pre	80	true
49.0ms	317×	body	640	valid
18.0ms	153×	body	320	valid
7.0ms	85×	body	160	valid