Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	299×	body	80	valid
6.0ms	104×	body	80	nan

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	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

localize17.0ms

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))

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×	`sqrt-div` `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 → 113

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

series1.4s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
30.0ms	(/ (* M D) (* 2.0 d))
351.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
672.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5002	994

prune359.0ms

Filtered

125 candidates to 81 candidates (64.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 7.8b

Counts

126 → 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)

rewrite28.0ms

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×	`associate-/r*` `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 → 96

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(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:

27.0ms	(/ (* M D) (* 2.0 d))
368.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
724.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
675.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	560	828
1	2559	746
2	5001	744

prune300.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 7.5b

Counts

114 → 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×	`associate-/r*` `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 → 146

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(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)
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
377.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
704.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
725.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify89.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	901	1943
1	3272	1558
2	5001	1548

prune337.0ms

Filtered

158 candidates to 71 candidates (44.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	157	8	165

Merged error: 7.5b

Counts

165 → 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×	`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 → 142

Calls

4 calls:

11.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
2.0ms	(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
16.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))

series1.4s

Counts

4 → 12

Calls

4 calls:

467.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
34.0ms	(/ (* M D) (* 2.0 d))
284.0ms	(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
628.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))

simplify130.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	877	1782
1	4503	1603
2	5002	1576

prune349.0ms

Filtered

154 candidates to 78 candidates (50.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	154	8	162

Merged error: 7.5b

Counts

162 → 8

regimes586.0ms

Accuracy

-4.4% (2.3b remaining)

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

bsearch136.0ms

Steps

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

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

561.0ms	9358×	body	80	valid
193.0ms	3103×	body	80	nan