Details

sample45.0ms

Algorithm

intervals

Results

17.0ms	292×	body	80	valid
6.0ms	98×	body	80	nan

simplify57.0ms

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: 16.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
13.6b	(* (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))

series1.5s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
359.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms	(/ (* M D) (* 2.0 d))
671.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify78.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (65.0ms)

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

prune435.0ms

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: 9.4b

Counts

134 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b	(/ (* 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:

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

728.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
689.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
369.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
31.0ms	(/ (* M D) (* 2.0 d))

simplify70.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	576	880
1	2585	798
2	5003	796

prune400.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	114	11	125

Merged error: 8.7b

Counts

125 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
30×	`add-cbrt-cube`
19×	`prod-exp`
16×	`add-sqr-sqrt`
12×	`div-exp`
10×	`*-un-lft-identity`
9×	`associate-l` `cbrt-unprod`
8×	`cbrt-undiv` `add-cube-cbrt`
6×	`unpow-prod-down`
5×	`pow1` `pow-exp` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `div-inv` `unswap-sqr`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 98

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series1.1s

Counts

4 → 12

Calls

4 calls:

359.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
715.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
32.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

simplify62.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	457	980
1	1916	875
2	5001	873

prune580.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 8.7b

Counts

121 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.6b	(* (* M D) (/ 1 (* 2.0 d)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
42×	`prod-exp`
39×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt` `associate-r` `associate-l`
8×	`cbrt-undiv`
6×	`unpow-prod-down`
5×	`times-frac` `pow-exp` `sqrt-prod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (* M D) (/ 1 (* 2.0 d)))

series1.1s

Counts

4 → 12

Calls

4 calls:

352.0ms	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
702.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(* (* M D) (/ 1 (* 2.0 d)))

simplify80.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	656	1100
1	3130	965
2	5002	961

prune380.0ms

Filtered

129 candidates to 76 candidates (58.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	130	9	139

Merged error: 8.7b

Counts

139 → 9

regimes878.0ms

Accuracy

0% (1.6b remaining)

Error of 9.3b against oracle of 7.7b and baseline of 9.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	17
1	32	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

578.0ms	9356×	body	80	valid
186.0ms	3083×	body	80	nan