Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
5.0ms	229×	body	80	nan
5.0ms	36×	body	1280	valid
3.0ms	135×	body	80	valid
1.0ms	17×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 19.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
974×	`*-un-lft-identity`
817×	`add-sqr-sqrt`
787×	`add-cube-cbrt`
649×	`sqrt-prod`
594×	`prod-diff`
175×	`associate-/r*`
156×	`frac-sub`
85×	`distribute-lft-out`
81×	`associate-/l*`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
27×	`frac-2neg` `clear-num`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 894

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
56.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series272.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ 1.0 (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (sqrt x))
147.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify257.0ms

Algorithm

egg-herbie

Counts

903 → 903

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2575	27701
1	5001	23030

prune1.5s

Filtered

903 candidates to 450 candidates (50.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	890	13	903
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	891	13	904

Merged error: 19.1b

Counts

904 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
1.9b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite10.0s

Algorithm

rewrite-expression-head

Rules

64220×	`associate-/r*`
57242×	`frac-times`
55191×	`*-un-lft-identity`
51442×	`add-sqr-sqrt`
46332×	`sqrt-prod`
41586×	`add-cube-cbrt`
33490×	`frac-sub`
30098×	`associate-/l*`
21578×	`times-frac`
10278×	`clear-num`
9910×	`frac-2neg`
9202×	`prod-diff`
6610×	`swap-sqr`
6323×	`distribute-lft-out`
4744×	`associate-l`
4720×	`associate-r`
4586×	`associate-r/` `associate-l/`
2061×	`unswap-sqr`
788×	`div-inv`
736×	`un-div-inv`
688×	`sqrt-div` `associate-/r/`
344×	`flip3-+` `flip-+`
289×	`difference-of-squares`
229×	`*-commutative`
86×	`fma-neg`
31×	`distribute-lft-out--`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 43468

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
24.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.1s	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt x))
39.0ms	(/ 1.0 (sqrt x))
33.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
63.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify17.1s

Algorithm

egg-herbie

Counts

43480 → 43480

Iterations

Useful iterations: 0 (1.0s)

Iter	Nodes	Cost
0	42439	1849256

prune1.5m

Filtered

43480 candidates to 18754 candidates (56.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	43472	8	43480
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	43482	11	43493

Merged error: 5.9b

Counts

43493 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
1.9b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite7.0s

Algorithm

rewrite-expression-head

Rules

99678×	`sqrt-div`
51690×	`associate-/r*`
34559×	`*-un-lft-identity`
33689×	`sqrt-prod`
26476×	`add-sqr-sqrt`
26378×	`add-cube-cbrt`
24964×	`frac-times`
24960×	`frac-sub`
24804×	`frac-add`
23931×	`associate-/l*`
7977×	`frac-2neg` `clear-num`
4074×	`distribute-lft-out`
3335×	`times-frac`
2250×	`prod-diff`
752×	`distribute-rgt-in` `distribute-lft-in`
234×	`flip3-+` `flip-+`
174×	`div-inv`
160×	`flip3--` `flip--`
158×	`associate-r/` `associate-l/`
150×	`associate-/r/`
32×	`difference-of-squares`
31×	`associate-r`
25×	`fma-neg`
24×	`distribute-lft-out--`
15×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg`
2×	`cbrt-undiv` `div-exp`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 27899

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
12.0ms	(/ 1.0 (sqrt x))
686.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
66.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series989.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt x))
42.0ms	(/ 1.0 (sqrt x))
613.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
295.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify11.2s

Algorithm

egg-herbie

Counts

27911 → 27911

Iterations

Useful iterations: 0 (912.0ms)

Iter	Nodes	Cost
0	17439	1409806

prune1.3m

Filtered

27911 candidates to 12327 candidates (55.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	27905	6	27911
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	27914	8	27922

Merged error: 5.9b

Counts

27922 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
0.2b	(/ (* (+ (* (sqrt (/ 1.0 1)) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite31.0s

Algorithm

rewrite-expression-head

Rules

441196×	`sqrt-div`
144877×	`associate-/r*`
119420×	`frac-times`
99056×	`sqrt-prod`
92527×	`*-un-lft-identity`
79040×	`associate-*r/`
74252×	`associate-/l/`
73776×	`frac-add`
73589×	`add-sqr-sqrt`
73008×	`frac-sub`
71880×	`associate-/l*`
70398×	`add-cube-cbrt`
25626×	`flip3-+` `flip-+`
23946×	`frac-2neg` `clear-num`
23362×	`associate-*l/`
10675×	`distribute-lft-out`
4289×	`times-frac`
1877×	`associate-r`
983×	`associate-l`
750×	`prod-diff`
656×	`difference-of-squares`
607×	`unswap-sqr`
492×	`distribute-lft-out--`
468×	`flip3--` `flip--`
141×	`div-inv`
87×	`*-commutative`
54×	`associate-/r/`
25×	`fma-neg`
20×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down`
2×	`sqrt-pow1` `pow1/2`
1×	`sub-neg` `sqrt-unprod` `diff-log`

Counts

4 → 77222

Calls

4 calls:

21.0ms	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
5.8s	(/ (* (+ (* (sqrt (/ 1.0 1)) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
4.0ms	(/ 1.0 (sqrt x))
61.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
1.2s	(/ (* (+ (* (sqrt (/ 1.0 1)) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
40.0ms	(/ 1.0 (sqrt x))
287.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify20.9s

Algorithm

egg-herbie

Counts

77234 → 77234

Iterations

Useful iterations: 0 (586.0ms)

Iter	Nodes	Cost
0	30550	2313107

prune5.5m

Filtered: 77234 candidates to 33754 candidates (56.3%)