Details

sample77.0ms

Algorithm

intervals

Results

15.0ms	303×	body	80	nan
9.0ms	167×	body	80	valid
7.0ms	27×	body	1280	valid
6.0ms	30×	body	640	valid
5.0ms	22×	body	1280	nan
5.0ms	23×	body	640	nan
3.0ms	18×	body	320	valid
2.0ms	16×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify85.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize27.0ms

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)
11.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite66.0ms

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:

24.0ms	(/ (* (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:

433.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
47.0ms	(* (sqrt 2.0) t)
217.0ms	(- (* (/ (+ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

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

prune302.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.7b	(/ (pow l 2) x)
9.6b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite33.0ms

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
24.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune441.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* l (/ l x)))
4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.6b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite33.0ms

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) (* l (/ l x)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
4.0ms	(/ (pow t 2) x)
13.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (pow t 2) (* l (/ l x)))
70.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
19.0ms	(/ (pow t 2) x)
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5001	855

prune337.0ms

Filtered

104 candidates to 74 candidates (71.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
4.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
9.6b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite30.0ms

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

series303.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
74.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
19.0ms	(/ (pow t 2) x)
164.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	499	1468
1	2115	1360
2	5002	1357

prune372.0ms

Filtered

104 candidates to 76 candidates (73.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.5b

regimes429.0ms

Accuracy

72.6% (6.5b remaining)

Error of 10.2b against oracle of 3.7b and baseline of 27.4b

bsearch739.0ms

Steps

Iters	Range		Point
7	7.270221721791219e+55	2.250025987616623e+57	1.7340539270701175e+57
8	1.9328499358604982e-162	5.417062397217011e-158	2.220972928848495e-162
9	1.2605780682660474e-272	3.7712679044064278e-264	3.279407962174291e-264
9	-1.235648397955762e-295	-2.4005261901403727e-301	-1.2175132025148866e-295
8	-2.617151391070889e-146	-5.418487111431146e-151	-5.511170609100405e-151
10	-5.392881571352004e+16	-30.883936201328435	-30300791297250332.0

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	130
1	79	130
2	82	130
3	82	130

end0.0ms

sample2.1s

Algorithm

intervals

Results

488.0ms	10115×	body	80	nan
273.0ms	5122×	body	80	valid
223.0ms	861×	body	1280	valid
200.0ms	1008×	body	640	valid
140.0ms	585×	body	1280	nan
115.0ms	614×	body	640	nan
97.0ms	674×	body	320	valid
50.0ms	349×	body	320	nan
35.0ms	335×	body	160	valid
18.0ms	178×	body	160	nan