Details

sample64.0ms

Algorithm

intervals

Results

28.0ms	780×	body	80	nan
11.0ms	286×	body	80	valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	10

prune5.0ms

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: 0.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
137×	`sqrt-prod`
121×	`times-frac`
105×	`*-un-lft-identity`
94×	`associate-l`
81×	`add-cube-cbrt`
62×	`associate-r`
36×	`associate-/r*`
26×	`associate-*l/`
20×	`difference-of-squares`
16×	`unswap-sqr`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1` `*-commutative`
10×	`distribute-lft-out--`
8×	`associate-*r/`
6×	`flip3--` `sqrt-div` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `frac-times` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `clear-num` `div-inv` `distribute-lft-out`
1×	`pow1/2`

Counts

4 → 265

Calls

4 calls:

46.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
26.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
14.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
209.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
162.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1119	2573
1	5001	2458

prune659.0ms

Filtered

277 candidates to 219 candidates (20.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	271	6	277
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	6	278

Merged error: 0b

Counts

278 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

857×	`times-frac`
850×	`add-sqr-sqrt`
615×	`sqrt-prod`
552×	`*-un-lft-identity`
542×	`associate-l`
483×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
464×	`add-cube-cbrt`
379×	`associate-r`
86×	`difference-of-squares`
85×	`unswap-sqr`
84×	`*-commutative`
78×	`prod-diff`
61×	`neg-mul-1`
43×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out--`
40×	`associate-/r*`
19×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `div-exp` `associate-*l/` `associate-/r/` `distribute-neg-frac`
1×	`distribute-lft-neg-out` `frac-2neg` `pow1/2` `distribute-frac-neg` `clear-num` `distribute-lft-out`

Counts

4 → 1012

Calls

4 calls:

15.0ms	(* 9.0 (- a (/ 1.0 3.0)))
174.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
25.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
36.0ms	(/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 9.0 (- a (/ 1.0 3.0)))
130.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
213.0ms	(/ (* (- 1.0) rand) (- (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify215.0ms

Algorithm

egg-herbie

Counts

1024 → 1024

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3298	15583
1	5001	15247

prune2.3s

Filtered

1024 candidates to 656 candidates (35.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1022	2	1024
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	1025	5	1030

Merged error: 0b

Counts

1030 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))))
0.2b	(/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

4368×	`add-sqr-sqrt`
3542×	`associate-/l*`
2751×	`frac-times`
2492×	`*-un-lft-identity`
2205×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2078×	`add-cube-cbrt`
1991×	`cbrt-prod`
1770×	`associate-/r*`
1614×	`associate-l`
1522×	`sqrt-prod`
1278×	`associate-r`
1273×	`times-frac`
629×	`unswap-sqr`
576×	`swap-sqr`
408×	`difference-of-squares`
211×	`*-commutative`
204×	`distribute-lft-out--`
149×	`neg-mul-1`
112×	`clear-num`
111×	`frac-2neg`
69×	`associate-*l/`
43×	`associate-*r/`
41×	`add-cbrt-cube`
32×	`add-exp-log`
15×	`cbrt-unprod`
13×	`cbrt-undiv`
10×	`prod-exp`
9×	`pow1` `div-exp`
6×	`flip3--` `sqrt-div` `flip--`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-neg-frac` `add-log-exp`
3×	`flip3-+` `un-div-inv` `flip-+` `div-inv`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `distribute-lft-out`
1×	`distribute-lft-neg-out` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-frac-neg`

Counts

4 → 4072

Calls

4 calls:

12.0ms	(sqrt (- a (/ 1.0 3.0)))
1.6s	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))))
23.0ms	(/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0)))))
1.5s	(* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
209.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))))
175.0ms	(/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0)))))
320.0ms	(* (/ (- (* (cbrt 1.0) (cbrt 1.0))) (sqrt 9.0)) (/ (* (cbrt 1.0) rand) (- (sqrt (- a (/ 1.0 3.0))))))

simplify816.0ms

Algorithm

egg-herbie

Counts

4084 → 4084

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5001	80450

prune11.0s

Filtered

4084 candidates to 2394 candidates (41.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	4084	0	4084
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	4084	5	4089

Merged error: 0b

Counts

4089 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))))
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.2b	(/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))
0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

554×	`times-frac`
484×	`add-sqr-sqrt`
327×	`*-un-lft-identity`
323×	`sqrt-prod`
270×	`associate-l`
263×	`add-cube-cbrt`
62×	`difference-of-squares`
53×	`associate-/l*`
33×	`associate-/r*`
32×	`associate-*l/`
31×	`distribute-lft-out--`
28×	`associate-r`
25×	`unswap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`sqrt-div` `associate-/r/`
15×	`associate-/l/`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`*-commutative`
8×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*r/` `pow-prod-down`
1×	`distribute-lft-out`

Counts

4 → 507

Calls

4 calls:

85.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
30.0ms	(/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))
17.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)

series641.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))))
83.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
228.0ms	(/ (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (sqrt 9.0))
166.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)

simplify115.0ms

Algorithm

egg-herbie

Counts

519 → 519

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1793	6939
1	5002	6646

prune1.0s

Filtered

519 candidates to 312 candidates (39.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	519	0	519
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	519	5	524

Merged error: 0b

Counts

524 → 5

regimes69.0ms

Accuracy

0% (0.1b 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 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	27	12
2	28	12
3	28	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

914.0ms	26777×	body	80	nan
330.0ms	9124×	body	80	valid