Details

sample67.0ms

Algorithm

intervals

Results

20.0ms	297×	body	80	valid
7.0ms	101×	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

prune7.0ms

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: 14.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.1b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
14.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

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:

5.0ms	(* 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))))
5.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series536.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
145.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
209.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	738	1124
1	2959	1046
2	5001	1043

prune968.0ms

Filtered

125 candidates to 81 candidates (35.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 5.2b

Counts

126 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

3.1b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b	(/ (* M D) (* 2.0 d))
6.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

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)))
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
9.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series558.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms	(/ (* M D) (* 2.0 d))
200.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
208.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	693	925
1	2737	842
2	5002	840

prune972.0ms

Filtered

108 candidates to 70 candidates (35.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 4.6b

Counts

115 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))
7.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite43.0ms

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:

7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series419.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
209.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify82.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	1048	1799
1	3497	1375
2	5002	1371

prune1.5s

Filtered

162 candidates to 72 candidates (55.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	161	8	169

Merged error: 4.6b

Counts

169 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

3.1b	(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)))
6.1b	(/ M (/ (* 2.0 d) D))
6.4b	(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
7.8b	(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
55×	`add-exp-log`
50×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-l`
28×	`unpow-prod-down`
22×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
10×	`associate-/r*` `div-inv`
8×	`pow-exp`
7×	`cbrt-undiv`
5×	`pow1` `sqrt-prod`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r/` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 143

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)))
6.0ms	(/ M (/ (* 2.0 d) D))
11.0ms	(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
10.0ms	(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)

series539.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)))
6.0ms	(/ M (/ (* 2.0 d) D))
199.0ms	(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
209.0ms	(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) l)

simplify76.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	893	1234
1	3411	1157
2	5001	1155

prune3.0s

Filtered

155 candidates to 118 candidates (23.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	154	9	163

Merged error: 4.6b

Counts

163 → 9

regimes2.1s

Accuracy

26.3% (1.8b remaining)

Error of 9.0b against oracle of 7.2b and baseline of 9.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	34
1	43	34

end0.0ms

sample1.7s

Algorithm

intervals

Results

654.0ms	9352×	body	80	valid
225.0ms	3137×	body	80	nan

Details

sample67.0ms

simplify53.0ms

prune7.0ms

localize13.0ms

rewrite30.0ms

series536.0ms

simplify72.0ms

prune968.0ms

localize13.0ms

rewrite28.0ms

series558.0ms

simplify67.0ms

prune972.0ms

localize16.0ms

rewrite43.0ms

series419.0ms

simplify82.0ms

prune1.5s

localize18.0ms

rewrite36.0ms

series539.0ms

simplify76.0ms

prune3.0s

regimes2.1s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling