Details

sample68.0ms

Algorithm

intervals

Results

31.0ms	956×	body	80	nan
12.0ms	292×	body	80	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 0.1b

Counts

2 → 1

localize10.0ms

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)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

12.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
179.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
143.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune381.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	128	6	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 0.0b

Counts

135 → 6

localize10.0ms

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)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt` `prod-diff`
60×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-r`
9×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `sub-neg` `sqrt-pow1` `div-exp` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
16.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
12.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
187.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1157	3009
1	5002	2366

prune300.0ms

Filtered

195 candidates to 103 candidates (52.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	196	5	201

Merged error: 0.0b

Counts

201 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
0.4b	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
102×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-exp-log` `sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`associate-l`
26×	`prod-exp`
17×	`div-exp`
16×	`difference-of-squares` `unswap-sqr`
14×	`cbrt-unprod`
13×	`pow1`
9×	`cbrt-undiv` `associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*l/`
6×	`frac-times`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 217

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
18.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
27.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
76.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
212.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
181.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1219	2615
1	5002	2311

prune470.0ms

Filtered

229 candidates to 153 candidates (66.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	229	5	234

Merged error: 0.0b

Counts

234 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
0.3b	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
0.5b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
612×	`add-sqr-sqrt`
470×	`sqrt-prod`
456×	`*-un-lft-identity`
368×	`add-cube-cbrt`
203×	`associate-r`
88×	`difference-of-squares`
64×	`sqrt-div`
44×	`distribute-lft-out--`
36×	`associate-/l*`
32×	`flip3--` `flip--`
28×	`frac-times` `associate-/r/`
25×	`add-exp-log` `add-cbrt-cube`
16×	`div-inv`
15×	`associate-r/` `associate-/r`
12×	`associate-l`
11×	`pow1`
9×	`flip3-+` `flip-+`
8×	`associate-*l/`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 595

Calls

4 calls:

9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
54.0ms	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
18.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
19.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

series830.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
225.0ms	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
178.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
339.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

simplify137.0ms

Algorithm

egg-herbie

Counts

607 → 607

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2042	8131
1	5002	7591

prune1.2s

Filtered

607 candidates to 333 candidates (54.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	606	1	607
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	606	6	612

Merged error: 0.0b

Counts

612 → 6

regimes99.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

892.0ms	27046×	body	80	nan
320.0ms	9138×	body	80	valid