Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	196×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	19×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	7×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify8.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.4b

Counts

2 → 1

localize12.0ms

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)))))
13.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
15.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune679.0ms

Filtered

91 candidates to 67 candidates (26.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	12	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 12.9b

Counts

92 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `prod-exp` `flip-+`
3×	`sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
9.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	390	900
1	1684	818
2	5001	784

prune636.0ms

Filtered

100 candidates to 73 candidates (27.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Merged error: 12.9b

Counts

112 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.1b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
23×	`*-un-lft-identity`
22×	`times-frac`
21×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`log-pow` `unswap-sqr`
4×	`exp-prod` `sqrt-div` `prod-exp`
3×	`log-prod` `flip3-+` `associate-l` `flip-+`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
29.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	399	962
1	1650	873
2	5001	845

prune1.1s

Filtered

103 candidates to 81 candidates (21.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	101	14	115

Merged error: 12.9b

Counts

115 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

3.5b	(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
4.0b	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
13.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cbrt-cube`
15×	`associate-r`
13×	`add-cube-cbrt`
12×	`prod-exp`
11×	`pow1` `times-frac`
6×	`sqrt-prod` `cbrt-unprod` `add-log-exp`
4×	`flip3-+` `sqrt-div` `div-exp` `flip-+`
3×	`pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/r/`
1×	`+-commutative` `associate-r/` `associate-l` `sum-log` `un-div-inv` `sum-cubes` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

10.0ms	(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
12.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
8.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	444	869
1	2116	761
2	5002	743

prune1.6s

Filtered

98 candidates to 70 candidates (28.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	97	15	112

Merged error: 12.9b

Counts

112 → 15

regimes342.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32

end0.0ms

sample1.3s

Algorithm

intervals

Results

346.0ms	6020×	body	80	valid
262.0ms	790×	body	2560	valid
173.0ms	648×	body	1280	valid
135.0ms	8000×	pre	80	true
69.0ms	322×	body	640	valid
23.0ms	132×	body	320	valid
9.0ms	88×	body	160	valid

Details

sample50.0ms

simplify8.0ms

prune4.0ms

localize12.0ms

rewrite34.0ms

series34.0ms

simplify147.0ms

prune679.0ms

localize16.0ms

rewrite27.0ms

series61.0ms

simplify45.0ms

prune636.0ms

localize19.0ms

rewrite25.0ms

series60.0ms

simplify51.0ms

prune1.1s

localize29.0ms

rewrite35.0ms

series36.0ms

simplify62.0ms

prune1.6s

regimes342.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling