Details

sample83.0ms

Algorithm

intervals

Results

15.0ms	310×	body	80	nan
11.0ms	28×	body	640	nan
8.0ms	157×	body	80	valid
7.0ms	29×	body	1280	valid
6.0ms	24×	body	1280	nan
6.0ms	30×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	22×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	4×	body	160	nan

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize19.0ms

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)
14.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(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)
12.0ms	(- (* (/ (+ 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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

441.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (sqrt 2.0) t)
223.0ms	(- (* (/ (+ 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	1207
1	2051	1099
2	5002	1094

prune322.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.7b

localize23.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.1b	(/ (pow l 2) x)
9.6b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

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:

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

series278.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* 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)
170.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

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

prune488.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.6b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
4.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt 2.0) t)
69.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
18.0ms	(/ (pow t 2) x)
166.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	480	1048
1	2213	963
2	5001	954

prune410.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sqrt 2.0) t)) (cbrt (* (sqrt 2.0) t)))
2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.6b	(/ (pow t 2) x)
26.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`pow1/3` `add-cbrt-cube` `add-log-exp`
4×	`cbrt-prod` `flip3-+` `sqrt-div` `swap-sqr` `associate-r` `associate-l` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+r+` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`cbrt-undiv` `+-commutative` `pow2` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

6.0ms	(* (cbrt (* (sqrt 2.0) t)) (cbrt (* (sqrt 2.0) t)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
4.0ms	(/ (pow t 2) x)
13.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(* (cbrt (* (sqrt 2.0) t)) (cbrt (* (sqrt 2.0) t)))
69.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
19.0ms	(/ (pow t 2) x)
168.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	548	1123
1	2266	1023
2	5002	985

prune494.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.3b

regimes455.0ms

Accuracy

75% (6.1b remaining)

Error of 10.0b against oracle of 3.9b and baseline of 28.3b

bsearch202.0ms

Steps

Iters	Range		Point
8	1.80595587673263e-54	6.561292613698866e-51	6.437639390291024e-51
9	-2.6982004546836606e+112	-1.398310470605562e+107	-2.70678176523746e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	48
1	55	48
2	55	48

end0.0ms

sample2.1s

Algorithm

intervals

Results

489.0ms	10060×	body	80	nan
259.0ms	5132×	body	80	valid
210.0ms	846×	body	1280	valid
192.0ms	975×	body	640	valid
153.0ms	634×	body	1280	nan
118.0ms	619×	body	640	nan
101.0ms	665×	body	320	valid
50.0ms	364×	body	320	nan
37.0ms	382×	body	160	valid
17.0ms	190×	body	160	nan