Details

sample84.0ms

Algorithm

intervals

Results

25.0ms	308×	body	80	nan
9.0ms	174×	body	80	valid
6.0ms	30×	body	640	valid
6.0ms	22×	body	1280	valid
5.0ms	18×	body	1280	nan
4.0ms	18×	body	640	nan
3.0ms	21×	body	320	valid
2.0ms	10×	body	320	nan
1.0ms	9×	body	160	valid
1.0ms	7×	body	160	nan

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
10.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

16.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
18.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

422.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
43.0ms	(* (sqrt 2.0) t)
213.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	417	1208
1	2051	1099
2	5002	1094

prune293.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.4b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.5b	(/ (pow l 2) x)
10.0b	(/ (pow t 2) x)
28.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
9.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune433.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
10.0b	(/ (pow t 2) x)
28.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`cbrt-prod` `div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+r+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

1.0ms	(cbrt x)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
82.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms	(/ (pow t 2) x)
179.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	466	1168
1	1981	1076
2	5001	1068

prune386.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))
10.0b	(/ (pow t 2) x)
28.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`cbrt-prod` `div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+r+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

1.0ms	(cbrt x)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt x)
84.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))))))
18.0ms	(/ (pow t 2) x)
185.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	471	1581
1	2025	1465
2	5001	1451

prune410.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.5b

regimes443.0ms

Accuracy

74.2% (6.0b remaining)

Error of 9.7b against oracle of 3.7b and baseline of 27.1b

bsearch434.0ms

Steps

Iters	Range		Point
9	6.5674376860864575e+41	3.160563175756606e+48	2.439864779519815e+48
5	2.5314598921169833e-163	7.493051701410122e-163	6.30041024948343e-163
9	-6.02957645582761e-302	-2.832827517419726e-308	-2.8785002221205043e-308
9	-3.8796894483799902e+115	-4.972566247523887e+110	-2.4044001424157714e+115

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	102
1	75	102
2	78	102
3	78	102

end0.0ms

sample2.1s

Algorithm

intervals

Results

514.0ms	10071×	body	80	nan
273.0ms	5079×	body	80	valid
227.0ms	878×	body	1280	valid
201.0ms	1007×	body	640	valid
156.0ms	587×	body	1280	nan
120.0ms	600×	body	640	nan
99.0ms	666×	body	320	valid
52.0ms	355×	body	320	nan
39.0ms	370×	body	160	valid
18.0ms	187×	body	160	nan