Details

sample84.0ms

Algorithm

intervals

Results

23.0ms	303×	body	80	nan
8.0ms	167×	body	80	valid
7.0ms	27×	body	1280	valid
6.0ms	30×	body	640	valid
5.0ms	22×	body	1280	nan
4.0ms	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

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	14
1	101	14
2	234	14
3	525	14
4	1016	14
5	1701	14
6	3626	14
7	5002	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

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)
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)))

rewrite77.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

25.0ms	(/ (* (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))
31.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

408.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
209.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify65.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	446	1290
1	2206	1177
2	5002	1172

prune338.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
254.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	377	837
1	1450	724
2	5001	715

prune443.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.6b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
9.6b	(/ (pow t 2) x)
26.1b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite16.0ms

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×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt 2.0) t)
66.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
256.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	321	653
1	1261	592
2	5001	586

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
4.6b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
9.6b	(/ (pow t 2) x)
26.1b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

21.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
67.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
259.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	843
1	1422	691
2	5002	641

prune352.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.5b

regimes456.0ms

Accuracy

72% (6.6b remaining)

Error of 10.3b against oracle of 3.7b and baseline of 27.4b

bsearch703.0ms

Steps

Iters	Range		Point
7	7.270221721791219e+55	2.250025987616623e+57	2.2196746899374166e+57
8	1.9328499358604982e-162	5.417062397217011e-158	3.5772972405045893e-160
9	1.2605780682660474e-272	3.7712679044064278e-264	1.9763068281072403e-264
9	-1.235648397955762e-295	-2.4005261901403727e-301	-1.2175132025148866e-295
8	-2.617151391070889e-146	-5.418487111431146e-151	-5.511170609100405e-151
9	-0.00043085380315138777	-1.5019222372888607e-11	-0.00042495707652516766

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	138
1	75	138

end0.0ms

sample2.0s

Algorithm

intervals

Results

482.0ms	10115×	body	80	nan
256.0ms	5122×	body	80	valid
213.0ms	861×	body	1280	valid
199.0ms	1008×	body	640	valid
140.0ms	585×	body	1280	nan
113.0ms	614×	body	640	nan
96.0ms	674×	body	320	valid
47.0ms	349×	body	320	nan
32.0ms	335×	body	160	valid
18.0ms	178×	body	160	nan