Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	300×	body	80	valid
5.0ms	88×	body	80	nan

simplify55.0ms

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

prune4.0ms

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: 14.8b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.6b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.4b	(/ (* M D) (* 2.0 d))
10.5b	(* (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×	`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))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
363.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms	(/ (* M D) (* 2.0 d))
887.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (60.0ms)

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

prune404.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 8.1b

Counts

134 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.6b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b	(/ (* 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×	`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) l)
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms	(/ (* M D) (* 2.0 d))

series1.9s

Counts

4 → 12

Calls

4 calls:

378.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
717.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
745.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
28.0ms	(/ (* M D) (* 2.0 d))

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

prune338.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 7.5b

Counts

125 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.4b	(/ (* M D) (* 2.0 d))
5.4b	(/ (* M D) (* 2.0 d))
5.5b	(* (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` `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:

14.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
9.0ms	(/ (* 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:

722.0ms	(/ (* (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))
28.0ms	(/ (* M D) (* 2.0 d))
747.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify84.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	882	1759
1	3170	1336
2	5001	1332

prune384.0ms

Filtered

170 candidates to 80 candidates (47.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	166	4	170
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	170	10	180

Merged error: 7.0b

Counts

180 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
5.4b	(/ (* M D) (* 2.0 d))
5.4b	(/ (* M D) (* 2.0 d))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

10.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.3s

Counts

4 → 12

Calls

4 calls:

483.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
28.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))
753.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify70.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	562	1148
1	2358	1017
2	5001	1011

prune437.0ms

Filtered

138 candidates to 89 candidates (64.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	138	10	148

Merged error: 7.0b

Counts

148 → 10

regimes915.0ms

Accuracy

-16.3% (1.6b remaining)

Error of 8.8b against oracle of 7.3b and baseline of 8.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	76
1	56	76

end0.0ms

sample1.2s

Algorithm

intervals

Results

561.0ms	9299×	body	80	valid
192.0ms	3210×	body	80	nan