Details

sample110.0ms

Algorithm

intervals

Results

36.0ms	327×	body	80	nan
11.0ms	160×	body	80	valid
9.0ms	27×	body	1280	valid
9.0ms	29×	body	640	valid
6.0ms	23×	body	640	nan
6.0ms	27×	body	320	valid
5.0ms	14×	body	1280	nan
3.0ms	16×	body	320	nan
2.0ms	13×	body	160	valid
0.0ms	2×	body	160	nan

simplify90.0ms

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

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: 45.6b

Counts

2 → 1

localize20.0ms

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)
14.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite60.0ms

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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

414.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
42.0ms	(* (sqrt 2.0) t)
209.0ms	(- (* (/ (+ 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)))

simplify63.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

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

prune282.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 6.5b

Counts

93 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.7b	(/ (pow l 2) x)
9.8b	(/ (pow t 2) x)
29.5b	(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:

9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 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)
164.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

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

prune424.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 3.9b

Counts

146 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.8b	(/ (pow t 2) x)
29.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite29.0ms

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)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
161.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	478	927
1	2222	851
2	5002	848

prune327.0ms

Filtered

115 candidates to 79 candidates (68.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	115	11	126

Merged error: 3.8b

Counts

126 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
3.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.8b	(/ (pow t 2) x)
29.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
16×	`cbrt-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `unswap-sqr` `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`

Counts

4 → 121

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
8.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt x) (cbrt x))
83.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms	(/ (pow t 2) x)
180.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	520	1310
1	2335	1209
2	5001	1186

prune391.0ms

Filtered

133 candidates to 92 candidates (69.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	133	11	144

Merged error: 3.8b

Counts

144 → 11

regimes389.0ms

Accuracy

76.6% (5.5b remaining)

Error of 9.4b against oracle of 3.9b and baseline of 27.5b

bsearch475.0ms

Steps

Iters	Range		Point
7	1.6839693347299939e+97	1.6062080025132939e+99	1.014167889591779e+98
5	-8.812694604940712e-279	-3.4016243527689706e-279	-8.667237132201513e-279
11	-5.726183670523198e-185	-1.7504520051528286e-206	-2.9209855921545484e-185
8	-6.814393060070563e+87	-2.556375663268158e+85	-1.1695024815233902e+87

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	92
1	66	92

end0.0ms

sample2.7s

Algorithm

intervals

Results

692.0ms	10159×	body	80	nan
364.0ms	5082×	body	80	valid
292.0ms	869×	body	1280	valid
285.0ms	1027×	body	640	valid
196.0ms	592×	body	1280	nan
163.0ms	605×	body	640	nan
137.0ms	656×	body	320	valid
71.0ms	355×	body	320	nan
51.0ms	366×	body	160	valid
22.0ms	171×	body	160	nan

Details

sample110.0ms

simplify90.0ms

prune5.0ms

localize20.0ms

rewrite60.0ms

series1.8s

simplify63.0ms

prune282.0ms

localize17.0ms

rewrite33.0ms

series267.0ms

simplify64.0ms

prune424.0ms

localize16.0ms

rewrite29.0ms

series283.0ms

simplify71.0ms

prune327.0ms

localize21.0ms

rewrite31.0ms

series481.0ms

simplify72.0ms

prune391.0ms

regimes389.0ms

bsearch475.0ms

simplify3.0ms

end0.0ms

sample2.7s

Profiling