Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	247×	body	80	nan
5.0ms	54×	body	640	valid
4.0ms	31×	body	1280	valid
4.0ms	134×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	15×	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 (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: 21.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
4.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
48.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series255.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
141.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify264.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	1517	24924
1	4197	18301
2	5001	18266

prune1.0s

Filtered

748 candidates to 285 candidates (38.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	730	18	748
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	731	18	749

Merged error: 20.2b

Counts

749 → 18

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
4.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
58×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
42×	`prod-diff`
35×	`add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out`
7×	`pow1` `fma-neg` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 132

Calls

3 calls:

22.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series398.0ms

Counts

3 → 9

Calls

3 calls:

264.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify83.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	614	1715
1	2883	1280
2	5002	1185

prune259.0ms

Filtered

141 candidates to 76 candidates (53.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	141	18	159

Merged error: 19.8b

Counts

159 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
4.1b	(+ x (- 1.0 x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-cube-cbrt`
11×	`associate-+r+`
9×	`cbrt-undiv` `div-exp` `prod-diff` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `associate-/l/`
2×	`associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 156

Calls

4 calls:

14.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms	(+ x (- 1.0 x))

series704.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
495.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify108.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	799	1711
1	4236	1448
2	5001	1435

prune352.0ms

Filtered

168 candidates to 106 candidates (63.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	10	7	17
Picked	1	0	1
Done	0	0	0
Total	176	10	186

Merged error: 0.3b

Counts

186 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`sqrt-prod`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
22×	`distribute-lft-out`
21×	`add-cube-cbrt`
19×	`times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`fma-def` `associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
12.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series776.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
496.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	1320
1	3636	1120
2	5002	1050

prune264.0ms

Filtered

143 candidates to 94 candidates (65.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	136	7	143
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	141	12	153

Merged error: 0.0b

Counts

153 → 12

regimes49.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	16
1	19	16

end0.0ms

sample886.0ms

Algorithm

intervals

Results

191.0ms	8133×	body	80	nan
189.0ms	1849×	body	640	valid
148.0ms	1135×	body	1280	valid
108.0ms	4095×	body	80	valid
45.0ms	611×	body	320	valid
18.0ms	310×	body	160	valid