Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	245×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	14
1	93	14

prune8.0ms

Filtered

1 candidates to 1 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: 0.0b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 105

Calls

3 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
12.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
8.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify32.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5481	1959

prune217.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 0b

Counts

116 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
0.0b	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
80×	`times-frac`
78×	`exp-prod`
54×	`log-pow`
50×	`add-cube-cbrt`
30×	`associate-r`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
9×	`log-prod`
8×	`pow1` `add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
3×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `associate-l`
2×	`exp-diff` `associate-/l/`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
18.0ms	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
10.0ms	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
8.0ms	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
11.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5246	3212

prune316.0ms

Filtered

129 candidates to 183 candidates (-41.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	184	4	188

Merged error: 0b

Counts

188 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(* 6.0 (log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
0.0b	(log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
40×	`times-frac`
34×	`add-cube-cbrt`
26×	`pow-unpow`
21×	`log-prod`
12×	`unpow-prod-down`
11×	`add-exp-log` `distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube`
7×	`pow1` `distribute-rgt-in` `distribute-lft-in`
5×	`associate-/l*`
4×	`rem-log-exp` `associate-r` `pow-exp` `associate-/r*` `associate-/r/` `add-log-exp` `sqr-pow`
3×	`div-sub` `associate-l`
2×	`pow-to-exp` `e-exp-1` `flip3-+` `log-pow` `flip-+` `div-inv` `associate-/l/` `pow-sub`
1×	`cbrt-undiv` `log-div` `flip3--` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

8.0ms	(pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
5.0ms	(* 6.0 (log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
2.0ms	(log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
17.0ms	(* 6.0 (log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
13.0ms	(log (pow E (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5015	3084

prune272.0ms

Filtered

106 candidates to 153 candidates (-44.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0b

Counts

157 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt x) (sqrt 1.0))
0.0b	(* 6.0 (* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.2b	(/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.2b	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
73×	`times-frac`
62×	`sqrt-prod`
43×	`associate-r`
40×	`difference-of-squares`
35×	`add-cube-cbrt`
21×	`distribute-lft-out`
20×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
11×	`pow1`
9×	`associate-/l*`
8×	`associate-l`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`frac-times` `pow-prod-down` `associate-l/` `associate-/r` `associate-/r/`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `*-commutative` `flip--` `div-inv` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 176

Calls

4 calls:

5.0ms	(- (sqrt x) (sqrt 1.0))
18.0ms	(* 6.0 (* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
10.0ms	(/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
24.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (sqrt x) (sqrt 1.0))
34.0ms	(* 6.0 (* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
15.0ms	(/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
31.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4987	4376
1	4987	4376

prune301.0ms

Filtered

111 candidates to 188 candidates (-69.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	188	4	192

Merged error: 0b

Counts

192 → 4

regimes37.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample940.0ms

Algorithm

intervals

Results

352.0ms	8000×	body	80	valid
321.0ms	8097×	body	80	nan

Details

sample30.0ms

simplify4.0ms

prune8.0ms

localize12.0ms

rewrite28.0ms

series19.0ms

simplify32.0ms

prune217.0ms

localize13.0ms

rewrite53.0ms

series37.0ms

simplify49.0ms

prune316.0ms

localize14.0ms

rewrite29.0ms

series50.0ms

simplify41.0ms

prune272.0ms

localize12.0ms

rewrite65.0ms

series83.0ms

simplify58.0ms

prune301.0ms

regimes37.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample940.0ms

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