Details

sample49.0ms

Algorithm

intervals

Results

18.0ms	306×	body	80	valid
10.0ms	104×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.6b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.4b	(/ (* M D) (* 2.0 d))
11.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite35.0ms

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:

8.0ms	(* 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))))
4.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

405.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
369.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
685.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.4b	(/ (* M D) (* 2.0 d))
6.4b	(/ (* M D) (* 2.0 d))
8.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite31.0ms

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×	`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 → 110

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)))))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.3s

Counts

4 → 12

Calls

4 calls:

355.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
27.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
861.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	576	1133
1	2582	1013
2	5001	1012

prune400.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.4b	(/ (* M D) (* 2.0 d))
6.4b	(/ (* M D) (* 2.0 d))

rewrite45.0ms

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×	`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 → 134

Calls

4 calls:

12.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
17.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))

series1.4s

Counts

4 → 12

Calls

4 calls:

704.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
675.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
26.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

simplify75.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	701	1167
1	3217	993
2	5003	980

prune407.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (* M D) (* 2.0 d))
17.6b	(cbrt (/ (* M D) (* 2.0 d)))
17.6b	(cbrt (/ (* M D) (* 2.0 d)))
17.6b	(cbrt (/ (* M D) (* 2.0 d)))

rewrite14.0ms

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:

4.0ms	(/ (* M D) (* 2.0 d))
3.0ms	(cbrt (/ (* M D) (* 2.0 d)))
3.0ms	(cbrt (/ (* M D) (* 2.0 d)))
3.0ms	(cbrt (/ (* M D) (* 2.0 d)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
102.0ms	(cbrt (/ (* M D) (* 2.0 d)))
103.0ms	(cbrt (/ (* M D) (* 2.0 d)))
104.0ms	(cbrt (/ (* M D) (* 2.0 d)))

simplify34.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (28.0ms)

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

prune389.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

regimes767.0ms

Accuracy

-29.4% (2.0b remaining)

Error of 9.3b against oracle of 7.3b and baseline of 8.9b

bsearch55.0ms

Steps

Iters	Range		Point
0	-6.0706316482279e-314	-1.976262583365e-323	-3.0353158251021e-314
6	-4.4879316068299356e+294	-6.981255098223496e+293	-4.434769257142831e+294

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	38
1	39	38

end0.0ms

sample1.2s

Algorithm

intervals

Results

562.0ms	9329×	body	80	valid
196.0ms	3112×	body	80	nan