Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	306×	body	80	valid
7.0ms	103×	body	80	nan

simplify56.0ms

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

prune6.0ms

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: 13.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b	(/ (* M D) (* 2.0 d))
11.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

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))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

398.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
360.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
669.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (63.0ms)

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

prune346.0ms

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: 7.6b

Counts

126 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.7b	(/ (* M D) (* 2.0 d))

rewrite30.0ms

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)
10.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

series1.8s

Counts

4 → 12

Calls

4 calls:

370.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
716.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
674.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
27.0ms	(/ (* M D) (* 2.0 d))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

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

prune293.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 6.5b

Counts

114 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))
5.8b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite49.0ms

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:

18.0ms	(/ (* (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))
7.0ms	(* (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)
27.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))
732.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (70.0ms)

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

prune320.0ms

Filtered

162 candidates to 72 candidates (44.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	162	7	169

Merged error: 6.5b

Counts

169 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)
5.7b	(/ (* M D) (* 2.0 d))
5.8b	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
6.4b	(* (/ M 2.0) (/ D d))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

13.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
10.0ms	(* (/ M 2.0) (/ D d))

series1.5s

Counts

4 → 12

Calls

4 calls:

705.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)
27.0ms	(/ (* M D) (* 2.0 d))
718.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
27.0ms	(* (/ M 2.0) (/ D d))

simplify108.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1129	1844
1	4460	1461
2	5001	1387

prune422.0ms

Filtered

186 candidates to 94 candidates (50.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	186	7	193

Merged error: 5.8b

Counts

193 → 7

regimes1.0s

Accuracy

7.6% (1.5b remaining)

Error of 8.4b against oracle of 6.9b and baseline of 8.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	50
1	52	50

end0.0ms

sample1.4s

Algorithm

intervals

Results

674.0ms	9278×	body	80	valid
225.0ms	2969×	body	80	nan

Details

sample52.0ms

simplify56.0ms

prune6.0ms

localize15.0ms

rewrite28.0ms

series1.5s

simplify76.0ms

prune346.0ms

localize13.0ms

rewrite30.0ms

series1.8s

simplify64.0ms

prune293.0ms

localize16.0ms

rewrite49.0ms

series1.5s

simplify88.0ms

prune320.0ms

localize20.0ms

rewrite51.0ms

series1.5s

simplify108.0ms

prune422.0ms

regimes1.0s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling