Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	288×	body	80	valid
7.0ms	90×	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	182	9
3	456	9
4	1557	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: 13.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.1b	(/ (* M D) (* 2.0 d))
10.5b	(* (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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `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 → 121

Calls

4 calls:

6.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms	(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))

series1.4s

Counts

4 → 12

Calls

4 calls:

394.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
351.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms	(/ (* M D) (* 2.0 d))
645.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5002	1054

prune390.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 6.2b

Counts

134 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

2.8b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b	(/ (* M D) (* 2.0 d))
7.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite31.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `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 → 104

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.8s

Counts

4 → 12

Calls

4 calls:

369.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
730.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
29.0ms	(/ (* M D) (* 2.0 d))
691.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify69.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	576	880
1	2585	798
2	5001	796

prune327.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Merged error: 5.4b

Counts

124 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* M D) (* 2.0 d))
6.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite50.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 158

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
15.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.5s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
722.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
689.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify87.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	882	1759
1	3170	1336
2	5002	1332

prune361.0ms

Filtered

170 candidates to 80 candidates (47.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Merged error: 5.1b

Counts

179 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l))
5.1b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* M D) (* 2.0 d))
6.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
9×	`times-frac` `associate-l`
8×	`associate-/r*`
6×	`cbrt-prod` `unpow-prod-down`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 114

Calls

4 calls:

10.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt 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:

718.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l))
33.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
739.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify71.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	531	962
1	2367	835
2	5001	835

prune408.0ms

Filtered

126 candidates to 86 candidates (68.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Merged error: 5.1b

Counts

134 → 8

regimes795.0ms

Accuracy

0% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms

sample1.4s

Algorithm

intervals

Results

730.0ms	9385×	body	80	valid
242.0ms	3138×	body	80	nan

Details

sample48.0ms

simplify53.0ms

prune3.0ms

localize17.0ms

rewrite29.0ms

series1.4s

simplify76.0ms

prune390.0ms

localize14.0ms

rewrite31.0ms

series1.8s

simplify69.0ms

prune327.0ms

localize17.0ms

rewrite50.0ms

series1.5s

simplify87.0ms

prune361.0ms

localize21.0ms

rewrite34.0ms

series1.5s

simplify71.0ms

prune408.0ms

regimes795.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Profiling