Details

sample70.0ms

Algorithm

intervals

Results

14.0ms	196×	body	80	valid
8.0ms	21×	body	2560	valid
7.0ms	19×	body	1280	valid
6.0ms	256×	pre	80	true
2.0ms	7×	body	640	valid
2.0ms	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

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

rewrite30.0ms

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))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

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)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify143.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (26.0ms)

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

prune868.0ms

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

localize12.0ms

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)))

rewrite29.0ms

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:

4.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
15.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(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)))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

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

prune646.0ms

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

localize16.0ms

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)))

rewrite28.0ms

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:

16.0ms	(* 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))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms	(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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	399	962
1	1650	851
2	5002	816

prune971.0ms

Filtered

103 candidates to 76 candidates (26.2%)

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

localize28.0ms

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)))

rewrite36.0ms

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))
13.0ms	(* (* 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)))

series37.0ms

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)))

simplify63.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (54.0ms)

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

prune1.4s

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

regimes315.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	32
1	39	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

300.0ms	6020×	body	80	valid
239.0ms	790×	body	2560	valid
154.0ms	648×	body	1280	valid
121.0ms	8000×	pre	80	true
60.0ms	322×	body	640	valid
20.0ms	132×	body	320	valid
8.0ms	88×	body	160	valid

Details

sample70.0ms

simplify8.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series37.0ms

simplify143.0ms

prune868.0ms

localize12.0ms

rewrite29.0ms

series58.0ms

simplify47.0ms

prune646.0ms

localize16.0ms

rewrite28.0ms

series58.0ms

simplify46.0ms

prune971.0ms

localize28.0ms

rewrite36.0ms

series37.0ms

simplify63.0ms

prune1.4s

regimes315.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling