Details

sample84.0ms

Algorithm

intervals

Results

41.0ms	933×	body	80	nan
16.0ms	294×	body	80	valid

simplify102.0ms

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

prune4.0ms

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

localize15.0ms

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)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite58.0ms

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)))
16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
177.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
142.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
73.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (77.0ms)

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

prune360.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

794×	`times-frac`
600×	`add-sqr-sqrt`
446×	`sqrt-prod`
436×	`*-un-lft-identity`
344×	`add-cube-cbrt`
210×	`associate-l`
92×	`difference-of-squares`
46×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-r`
5×	`flip3--` `flip--`
4×	`frac-times` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`expm1-log1p-u` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/l/`

Counts

3 → 513

Calls

3 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
43.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
17.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series551.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
216.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
179.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

522 → 522

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1655	6632
1	5001	6366

prune1.1s

Filtered

522 candidates to 317 candidates (60.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	521	1	522
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	521	7	528

Merged error: 0.0b

Counts

528 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.7b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 119

Calls

4 calls:

14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
13.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series585.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
153.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
169.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify92.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	787	1286
1	3151	1135
2	5002	1129

prune335.0ms

Filtered

131 candidates to 107 candidates (81.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	132	6	138

Merged error: 0.0b

Counts

138 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.2b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`associate-*l/`
8×	`associate-*r/` `sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 123

Calls

4 calls:

20.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
31.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
19.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
34.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
159.0ms	(* (* (- a (/ 1.0 3.0)) (/ 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))))

simplify89.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	758	1394
1	3358	1232
2	5001	1226

prune335.0ms

Filtered

135 candidates to 110 candidates (81.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	135	6	141

Merged error: 0b

Counts

141 → 6

regimes235.0ms

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	13
1	17	13

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	27323×	body	80	nan
419.0ms	9129×	body	80	valid