Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	298×	body	80	valid
7.0ms	91×	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

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: 10.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.8b	(/ (* M D) (* 2.0 d))
9.8b	(* (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×	`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)))))
2.0ms	(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:

409.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
360.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms	(/ (* M D) (* 2.0 d))
674.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5001	994

prune346.0ms

Filtered

125 candidates to 81 candidates (64.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 4.9b

Counts

126 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
3.9b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.8b	(/ (* 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×	`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)))
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	(/ (* M D) (* 2.0 d))

series1.8s

Counts

4 → 12

Calls

4 calls:

355.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
728.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
680.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
27.0ms	(/ (* M D) (* 2.0 d))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

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

prune291.0ms

Filtered

108 candidates to 68 candidates (63.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Merged error: 4.4b

Counts

117 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (* M D) (* 2.0 d))
18.4b	(cbrt (/ (* M D) (* 2.0 d)))
18.4b	(cbrt (/ (* M D) (* 2.0 d)))
18.4b	(cbrt (/ (* M D) (* 2.0 d)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
15×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 63

Calls

4 calls:

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

series340.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
102.0ms	(cbrt (/ (* M D) (* 2.0 d)))
107.0ms	(cbrt (/ (* M D) (* 2.0 d)))
102.0ms	(cbrt (/ (* M D) (* 2.0 d)))

simplify35.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	246	502
1	1144	440
2	5002	434

prune333.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	75	11	86

Merged error: 4.4b

Counts

86 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
3.0b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
5.8b	(/ (* M D) (* 2.0 d))
6.3b	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-exp-log`
85×	`div-exp`
79×	`prod-exp`
57×	`times-frac`
55×	`add-sqr-sqrt`
33×	`add-cbrt-cube`
30×	`pow-exp`
25×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r`
18×	`unpow-prod-down`
13×	`cbrt-undiv` `cbrt-prod` `associate-l` `cbrt-unprod`
12×	`unswap-sqr`
10×	`associate-/l*`
7×	`pow1` `div-inv`
6×	`pow-to-exp` `sqr-pow`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 176

Calls

4 calls:

9.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
2.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
6.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

466.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
402.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
34.0ms	(/ (* M D) (* 2.0 d))
723.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify118.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1043	2333
1	4913	2148
2	5001	2148

prune695.0ms

Filtered

188 candidates to 121 candidates (64.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	190	9	199

Merged error: 4.1b

Counts

199 → 9

regimes785.0ms

Accuracy

34.7% (2.1b remaining)

Error of 8.9b against oracle of 6.8b and baseline of 10.0b

bsearch191.0ms

Steps

Iters	Range		Point
10	4.455969450803597e-261	3.281697517885232e-249	5.331009994277483e-252
9	-2.177091376520771e+250	-1.640420445184289e+245	-1.6948917021138786e+245

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	30
1	44	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

690.0ms	9361×	body	80	valid
236.0ms	3061×	body	80	nan

Details

sample48.0ms

simplify54.0ms

prune3.0ms

localize16.0ms

rewrite28.0ms

series1.5s

simplify76.0ms

prune346.0ms

localize13.0ms

rewrite30.0ms

series1.8s

simplify67.0ms

prune291.0ms

localize18.0ms

rewrite20.0ms

series340.0ms

simplify35.0ms

prune333.0ms

localize17.0ms

rewrite45.0ms

series1.6s

simplify118.0ms

prune695.0ms

regimes785.0ms

bsearch191.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling