Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	295×	body	80	valid
5.0ms	97×	body	80	nan

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	182	9
3	456	9
4	1557	9
5	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0b	(/ (* M D) (* 2.0 d))
11.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite39.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `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 → 121

Calls

4 calls:

8.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms	(/ (* M D) (* 2.0 d))
18.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

397.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
353.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms	(/ (* M D) (* 2.0 d))
677.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5002	1054

prune418.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.0b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite34.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `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 → 104

Calls

4 calls:

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

series1.8s

Counts

4 → 12

Calls

4 calls:

358.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
707.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
26.0ms	(/ (* M D) (* 2.0 d))
691.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify63.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	576	880
1	2585	798
2	5001	796

prune363.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 158

Calls

4 calls:

10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
17.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.6s

Counts

4 → 12

Calls

4 calls:

708.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))
884.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify87.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	882	1759
1	3170	1336
2	5001	1332

prune433.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-exp-log`
34×	`div-exp` `prod-exp`
33×	`add-cbrt-cube`
16×	`add-sqr-sqrt` `unpow-prod-down`
15×	`pow-exp`
14×	`times-frac`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-/l`
10×	`cbrt-undiv` `cbrt-unprod`
9×	`associate-l`
6×	`div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `frac-2neg` `associate-r` `clear-num` `associate-/r*` `unswap-sqr`
1×	`*-commutative`

Counts

4 → 126

Calls

4 calls:

9.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
8.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(/ (* M D) (* 2.0 d))

series1.3s

Counts

4 → 12

Calls

4 calls:

484.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
746.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))

simplify74.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	562	1148
1	2358	1017
2	5001	1011

prune530.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

regimes905.0ms

Accuracy

0% (1.3b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 8.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

501.0ms	9408×	body	80	valid
175.0ms	3219×	body	80	nan