Details

sample91.0ms

Algorithm

intervals

Results

22.0ms	297×	body	80	valid
15.0ms	126×	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	178	9
3	446	9
4	1530	9
5	5001	9

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 12.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.3b	(/ (* M D) (* 2.0 d))
10.7b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite27.0ms

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:

5.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series548.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
150.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
214.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	738	1124
1	2959	1046
2	5001	1043

prune239.0ms

Filtered

125 candidates to 81 candidates (35.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 6.4b

Counts

126 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.3b	(/ (* M D) (* 2.0 d))

rewrite26.0ms

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:

4.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

series567.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
200.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
210.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	693	924
1	2737	841
2	5002	839

prune206.0ms

Filtered

108 candidates to 70 candidates (35.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 5.6b

Counts

115 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.3b	(/ (* M D) (* 2.0 d))
6.3b	(/ (* M D) (* 2.0 d))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

352×	`add-exp-log`
173×	`prod-exp`
125×	`div-exp`
75×	`pow-exp`
37×	`add-cbrt-cube`
15×	`pow-to-exp`
11×	`cbrt-undiv` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-/r*` `sqrt-prod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

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)))
13.0ms	(/ (* (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))

series369.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
210.0ms	(/ (* (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))

simplify69.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	902	1830
1	2909	1431
2	5003	1425

prune199.0ms

Filtered

148 candidates to 61 candidates (58.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	148	8	156

Merged error: 5.6b

Counts

156 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
4.2b	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
4.8b	(* (/ M 2.0) (/ D d))
5.2b	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
41×	`add-sqr-sqrt`
26×	`prod-exp`
25×	`*-un-lft-identity` `times-frac`
23×	`add-cube-cbrt` `add-cbrt-cube`
20×	`div-exp`
18×	`associate-l`
16×	`associate-r`
10×	`pow-exp`
7×	`pow1`
6×	`cbrt-undiv` `cbrt-unprod` `unswap-sqr`
5×	`sqrt-prod`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`pow-to-exp` `sqrt-div` `*-commutative` `sqr-pow`
1×	`frac-times` `unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
5.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
10.0ms	(* (/ M 2.0) (/ D d))
6.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

series559.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
199.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.0ms	(* (/ M 2.0) (/ D d))
207.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

simplify72.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	832	1043
1	3170	960
2	5001	958

prune197.0ms

Filtered

132 candidates to 88 candidates (33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	132	8	140

Merged error: 5.6b

Counts

140 → 8

regimes1.9s

Accuracy

38.5% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 7.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	44
1	57	44

end0.0ms

sample1.7s

Algorithm

intervals

Results

703.0ms	9029×	body	80	valid
325.0ms	4018×	body	80	nan

Details

sample91.0ms

simplify54.0ms

prune5.0ms

localize14.0ms

rewrite27.0ms

series548.0ms

simplify73.0ms

prune239.0ms

localize16.0ms

rewrite26.0ms

series567.0ms

simplify66.0ms

prune206.0ms

localize19.0ms

rewrite37.0ms

series369.0ms

simplify69.0ms

prune199.0ms

localize14.0ms

rewrite29.0ms

series559.0ms

simplify72.0ms

prune197.0ms

regimes1.9s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.7s

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