Details

sample68.0ms

Algorithm

intervals

Results

30.0ms	831×	body	80	nan
10.0ms	294×	body	80	valid

simplify98.0ms

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

localize11.0ms

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

rewrite56.0ms

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:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
15.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
17.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
184.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
145.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify93.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (77.0ms)

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

prune367.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Merged error: 0.0b

Counts

135 → 7

localize11.0ms

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)))))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite66.0ms

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:

14.0ms	(* 9.0 (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 9.0 (- a (/ 1.0 3.0)))
122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
192.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune333.0ms

Filtered

195 candidates to 103 candidates (52.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	196	6	202

Merged error: 0.0b

Counts

202 → 6

localize12.0ms

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

9.0ms	(sqrt (- a (/ 1.0 3.0)))
13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
12.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
15.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt (- a (/ 1.0 3.0)))
180.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
256.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
91.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify122.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	806	1332
1	4131	1224
2	5001	1220

prune322.0ms

Filtered

128 candidates to 97 candidates (75.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	127	7	134

Merged error: 0b

Counts

134 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
126×	`add-sqr-sqrt`
102×	`sqrt-prod`
86×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 184

Calls

3 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
33.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
15.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series572.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt (- a (/ 1.0 3.0)))
156.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
372.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify118.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1016	2566
1	4544	2406
2	5001	2404

prune408.0ms

Filtered

193 candidates to 124 candidates (64.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	195	5	200

Merged error: 0b

Counts

200 → 5

regimes69.0ms

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	18	11
1	18	11

end0.0ms

sample1.9s

Algorithm

intervals

Results

934.0ms	27026×	body	80	nan
335.0ms	9108×	body	80	valid