Details

sample57.0ms

Algorithm

intervals

Results

26.0ms	302×	body	80	valid
8.0ms	98×	body	80	nan

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 13.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b	(/ (* M D) (* 2.0 d))
12.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
371.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
692.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune368.0ms

Filtered

125 candidates to 81 candidates (64.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 7.5b

Counts

126 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.6b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(/ (* M D) (* 2.0 d))
7.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

362.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
688.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
28.0ms	(/ (* M D) (* 2.0 d))
715.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify71.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	560	828
1	2559	746
2	5001	744

prune288.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 6.5b

Counts

114 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.9b	(/ (* M D) (* 2.0 d))
4.9b	(/ (* M D) (* 2.0 d))
7.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 150

Calls

4 calls:

19.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.5s

Counts

4 → 12

Calls

4 calls:

698.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
28.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
726.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify84.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	836	1701
1	3118	1278
2	5001	1274

prune328.0ms

Filtered

162 candidates to 72 candidates (44.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	160	7	167

Merged error: 6.3b

Counts

167 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* 2.0 d))
4.9b	(/ (* M D) (* 2.0 d))
5.6b	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
7.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
35×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
14×	`add-sqr-sqrt`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/l*`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/r*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 100

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.4s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
596.0ms	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
722.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	499	825
1	2259	694
2	5001	694

prune454.0ms

Filtered

112 candidates to 71 candidates (63.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Merged error: 6.3b

Counts

119 → 7

regimes525.0ms

Accuracy

0% (1.3b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	16
1	24	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

746.0ms	9329×	body	80	valid
256.0ms	3171×	body	80	nan