Details

sample159.0ms

Algorithm

intervals

Results

43.0ms	295×	body	80	nan
24.0ms	163×	body	80	valid
16.0ms	15×	body	640	nan
15.0ms	33×	body	640	valid
12.0ms	21×	body	1280	valid
10.0ms	30×	body	320	valid
10.0ms	18×	body	1280	nan
3.0ms	9×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	6×	body	160	nan

simplify87.0ms

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))))
0.4b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite73.0ms

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:

30.0ms	(/ (* (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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

424.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms	(* (sqrt 2.0) t)
212.0ms	(- (* (/ (+ 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)))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune321.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

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))))
4.5b	(/ (pow l 2) x)
9.3b	(/ (pow t 2) x)
27.7b	(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))))
4.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
13.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series270.0ms

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)
19.0ms	(/ (pow t 2) x)
166.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune486.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
9.3b	(/ (pow t 2) x)
27.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
4.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
53.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
18.0ms	(/ (pow t 2) x)
143.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	493	1099
1	2141	999
2	5001	996

prune406.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize24.0ms

Local error

Found 4 expressions with local error:

9.3b	(/ (pow t 2) x)
27.6b	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
27.6b	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
27.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

4.0ms	(/ (pow t 2) x)
8.0ms	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
8.0ms	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
15.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
50.0ms	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
45.0ms	(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
144.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	559	1688
1	1963	1609
2	5002	1606

prune448.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

regimes516.0ms

Accuracy

77.5% (5.5b remaining)

Error of 9.6b against oracle of 4.1b and baseline of 28.5b

bsearch313.0ms

Steps

Iters	Range		Point
10	1.1469398243808202e+81	1.1762467128593058e+94	5.412378818721003e+86
9	-9.998794794503373e+152	-2.0918958204800063e+146	-1.3548877250587483e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	68
1	63	68

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.4s	10142×	body	80	nan
755.0ms	5157×	body	80	valid
467.0ms	844×	body	1280	valid
425.0ms	960×	body	640	valid
324.0ms	602×	body	1280	nan
259.0ms	597×	body	640	nan
223.0ms	653×	body	320	valid
108.0ms	319×	body	320	nan
92.0ms	386×	body	160	valid
37.0ms	158×	body	160	nan