Details

sample142.0ms

Algorithm

intervals

Results

41.0ms	309×	body	80	nan
16.0ms	154×	body	80	valid
14.0ms	39×	body	640	valid
14.0ms	30×	body	1280	valid
12.0ms	25×	body	1280	nan
8.0ms	22×	body	640	nan
6.0ms	22×	body	320	valid
2.0ms	12×	body	160	nan
2.0ms	11×	body	160	valid
2.0ms	8×	body	320	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: 45.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
0.5b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
14.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

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:

5.0ms	(* (sqrt 2.0) t)
24.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
29.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
426.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
220.0ms	(- (* (/ (+ 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)))

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

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

prune309.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

3.7b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.3b	(/ (pow l 2) x)
9.3b	(/ (pow t 2) x)
28.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite32.0ms

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)))))

series269.0ms

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)
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

prune462.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (sqrt 2.0) t) (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))))
3.7b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.3b	(/ (pow t 2) x)
28.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

14.0ms	(/ (* (sqrt 2.0) t) (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))))
11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
4.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (* (sqrt 2.0) t) (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))))
67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
18.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	544	1642
1	2637	1485
2	5001	1476

prune436.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize26.0ms

Local error

Found 4 expressions with local error:

9.3b	(/ (pow t 2) x)
28.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))
28.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))
28.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

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))))))
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
164.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))
157.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	384	1302
1	1563	1240
2	5001	1237

prune603.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

regimes513.0ms

Accuracy

75.5% (5.8b remaining)

Error of 9.7b against oracle of 3.9b and baseline of 27.4b

bsearch934.0ms

Steps

Iters	Range		Point
10	2.93431907672103e+33	2.2751499328762104e+43	3.0890860106314964e+41
9	3.259559301848564e-230	2.9187828048320224e-222	4.0588751522494764e-230
10	1.8225108733483394e-283	3.128387530648835e-268	2.812190751433782e-269
7	-1.309735712265202e-248	-6.1447451134247286e-251	-7.158971193644144e-250
10	-5.21421466722245e-164	-2.34619512224237e-179	-2.398429761188533e-164
0	-7.918636126216888e+114	-7.662623262413979e+114	-7.790629694315434e+114

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	178
1	91	178

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.0s	9916×	body	80	nan
531.0ms	5022×	body	80	valid
418.0ms	889×	body	1280	valid
406.0ms	1086×	body	640	valid
259.0ms	574×	body	1280	nan
226.0ms	625×	body	640	nan
191.0ms	668×	body	320	valid
97.0ms	351×	body	320	nan
65.0ms	335×	body	160	valid
34.0ms	178×	body	160	nan