Details

sample47.0ms

Algorithm

intervals

Results

16.0ms	306×	body	80	valid
9.0ms	112×	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	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: 15.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.7b	(/ (* M D) (* 2.0 d))
6.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.4b	(* (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×	`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)))))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts

4 → 12

Calls

4 calls:

398.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
26.0ms	(/ (* M D) (* 2.0 d))
351.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
669.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify79.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5001	1054

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
4.7b	(/ (* M D) (* 2.0 d))
6.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
9.7b	(* (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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 118

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
359.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
680.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	595	1196
1	2618	1077
2	5001	1076

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.9b

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
5.4b	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))
6.5b	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
6.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-exp-log`
121×	`prod-exp`
43×	`div-exp`
33×	`add-cbrt-cube`
31×	`associate-r`
30×	`pow-exp`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-unprod`
9×	`cbrt-prod`
7×	`pow1` `cbrt-undiv`
6×	`pow-to-exp` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `associate-l` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `flip--` `associate-/l*`

Counts

4 → 150

Calls

4 calls:

4.0ms	(/ (* M D) (* 2.0 d))
56.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))
18.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* M D) (* 2.0 d))
792.0ms	(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))
457.0ms	(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
391.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	913	2167
1	4652	1929
2	5001	1898

prune523.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.9b

localize21.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
4.7b	(/ (* M D) (* 2.0 d))
5.4b	(* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
6.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-exp-log`
64×	`prod-exp`
40×	`add-cbrt-cube`
25×	`div-exp`
22×	`associate-r`
20×	`times-frac` `cbrt-unprod`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cbrt-undiv`
10×	`pow1` `pow-exp`
9×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `div-inv`
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/` `associate-l` `-commutative` `flip--`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
49.0ms	(* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
30.0ms	(/ (* M D) (* 2.0 d))
582.0ms	(* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
387.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt h) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	750	1684
1	3596	1472
2	5002	1450

prune436.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.9b

regimes904.0ms

Accuracy

-22.6% (2.8b remaining)

Error of 10.7b against oracle of 7.8b and baseline of 10.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	50
1	71	50

end0.0ms

sample1.2s

Algorithm

intervals

Results

510.0ms	9362×	body	80	valid
170.0ms	3001×	body	80	nan