Details

sample48.0ms

Algorithm

intervals

Results

20.0ms	299×	body	80	valid
6.0ms	104×	body	80	nan

simplify54.0ms

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: 14.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b	(/ (* M D) (* 2.0 d))
4.7b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0b	(* (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)))))
6.0ms	(/ (* M D) (* 2.0 d))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

391.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms	(/ (* M D) (* 2.0 d))
374.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
664.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify75.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5001	1054

prune367.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 7.8b

Counts

134 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* M D) (* 2.0 d))
4.7b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.5b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

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	(/ (* M D) (* 2.0 d))
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)
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.8s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
361.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
704.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
675.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (55.0ms)

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

prune320.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 7.5b

Counts

122 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* M D) (* 2.0 d))
4.7b	(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)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
7.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

361×	`add-exp-log`
180×	`prod-exp`
125×	`div-exp`
80×	`pow-exp`
27×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`pow-to-exp`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`unpow-prod-down`
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×	`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 → 154

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
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)))
14.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
369.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
686.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
739.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify88.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	952	2025
1	3336	1640
2	5001	1630

prune336.0ms

Filtered

166 candidates to 79 candidates (47.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	165	8	173

Merged error: 7.5b

Counts

173 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
4.2b	(/ (* M D) (* 2.0 d))
4.7b	(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
6.0b	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-exp-log`
121×	`prod-exp`
43×	`div-exp`
33×	`add-cbrt-cube`
31×	`associate-r`
30×	`pow-exp`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-unprod`
9×	`cbrt-prod`
7×	`pow1` `cbrt-undiv`
6×	`pow-to-exp` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `associate-l` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `flip--` `associate-/l*`

Counts

4 → 150

Calls

4 calls:

11.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
3.0ms	(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
17.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))

series1.6s

Counts

4 → 12

Calls

4 calls:

641.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
27.0ms	(/ (* M D) (* 2.0 d))
289.0ms	(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
609.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))

simplify118.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	888	1860
1	4534	1666
2	5001	1635

prune394.0ms

Filtered

162 candidates to 93 candidates (57.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	162	8	170

Merged error: 7.5b

Counts

170 → 8

regimes530.0ms

Accuracy

-4.4% (2.3b remaining)

Error of 9.7b against oracle of 7.3b and baseline of 9.6b

bsearch138.0ms

Steps

Iters	Range		Point
7	-3.99728445701743e-234	-1.4437817457623158e-235	-7.74341334613102e-235
11	-2.4967893442235184e+300	-4.808678404789684e+277	-2.4720984130882936e+300

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

547.0ms	9358×	body	80	valid
191.0ms	3103×	body	80	nan