Details

sample46.0ms

Algorithm

intervals

Results

17.0ms	303×	body	80	valid
7.0ms	126×	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: 13.3b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.7b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.1b	(/ (* M D) (* 2.0 d))
9.7b	(* (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×	`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))

series1.5s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* 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))
683.0ms	(* (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

prune370.0ms

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: 7.2b

Counts

134 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.1b	(/ (* M D) (* 2.0 d))
4.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.6b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite29.0ms

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)))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(* (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:

361.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
33.0ms	(/ (* M D) (* 2.0 d))
704.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
681.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify68.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (57.0ms)

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

prune305.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Merged error: 7.0b

Counts

122 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
4.1b	(/ (* M D) (* 2.0 d))
4.1b	(/ (* M D) (* 2.0 d))
10.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* (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))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (- 1.0 (* (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))
694.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	595	1196
1	2618	1077
2	5001	1076

prune384.0ms

Filtered

130 candidates to 85 candidates (65.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	130	6	136

Merged error: 7.0b

Counts

136 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* M D) (* 2.0 d))
4.1b	(/ (* M D) (* 2.0 d))
6.0b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
8.0b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-exp-log`
95×	`prod-exp`
44×	`div-exp`
42×	`add-cbrt-cube`
25×	`pow-exp`
19×	`add-sqr-sqrt`
16×	`associate-r`
15×	`cbrt-unprod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`cbrt-undiv` `associate-l`
8×	`rec-exp` `1-exp`
6×	`pow1` `unpow-prod-down`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 142

Calls

4 calls:

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) (/ 1 l))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.5s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(/ (* M D) (* 2.0 d))
688.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
733.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify81.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	712	1215
1	3226	1041
2	5001	1028

prune370.0ms

Filtered

154 candidates to 83 candidates (53.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	154	6	160

Merged error: 7.0b

Counts

160 → 6

regimes658.0ms

Accuracy

-30.3% (1.7b remaining)

Error of 9.0b against oracle of 7.4b and baseline of 8.6b

bsearch96.0ms

Steps

Iters	Range		Point
0	-6.4228533959362e-323	0.0	-3.4584595208887e-323
11	-inf.0	-2.1021638254678998e+288	-1.7831495695640391e+308

simplify2.0ms

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

562.0ms	9375×	body	80	valid
193.0ms	3087×	body	80	nan