Details

sample56.0ms

Algorithm

intervals

Results

22.0ms	292×	body	80	valid
6.0ms	83×	body	80	nan

simplify51.0ms

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: 14.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.3b	(/ (* M D) (* 2.0 d))
12.2b	(* (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))

series580.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
159.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
225.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

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

prune280.0ms

Filtered

125 candidates to 81 candidates (35.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	11	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 7.2b

Counts

126 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
4.2b	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
4.3b	(/ (* M D) (* 2.0 d))
4.9b	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))

rewrite47.0ms

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:

2.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
20.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
233.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
6.0ms	(/ (* M D) (* 2.0 d))
328.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))

simplify46.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1203	2462
1	5001	2283

prune411.0ms

Filtered

188 candidates to 122 candidates (35.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 6.7b

Counts

199 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* M D) (* 2.0 d))
19.8b	(cbrt (/ (* M D) (* 2.0 d)))
19.8b	(cbrt (/ (* M D) (* 2.0 d)))
19.8b	(cbrt (/ (* M D) (* 2.0 d)))

rewrite21.0ms

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:

7.0ms	(/ (* 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)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
36.0ms	(cbrt (/ (* M D) (* 2.0 d)))
26.0ms	(cbrt (/ (* M D) (* 2.0 d)))
24.0ms	(cbrt (/ (* M D) (* 2.0 d)))

simplify34.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	258	520
1	1204	458
2	5002	452

prune287.0ms

Filtered

75 candidates to 62 candidates (17.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	75	12	87

Merged error: 6.7b

Counts

87 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.3b	(/ (* M D) (* 2.0 d))
4.4b	(* (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:

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

series615.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms	(/ (* M D) (* 2.0 d))
219.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
228.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

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

prune227.0ms

Filtered

108 candidates to 69 candidates (36.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	109	11	120

Merged error: 6.5b

Counts

120 → 11

regimes2.3s

Accuracy

-4.7% (2.1b remaining)

Error of 9.5b against oracle of 7.3b and baseline of 9.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	38
1	54	38

end0.0ms

sample1.7s

Algorithm

intervals

Results

703.0ms	9296×	body	80	valid
230.0ms	2987×	body	80	nan

Details

sample56.0ms

simplify51.0ms

prune5.0ms

localize18.0ms

rewrite28.0ms

series580.0ms

simplify74.0ms

prune280.0ms

localize22.0ms

rewrite47.0ms

series732.0ms

simplify46.0ms

prune411.0ms

localize27.0ms

rewrite21.0ms

series93.0ms

simplify34.0ms

prune287.0ms

localize15.0ms

rewrite28.0ms

series615.0ms

simplify63.0ms

prune227.0ms

regimes2.3s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling