Details

sample88.0ms

Algorithm

intervals

Results

43.0ms	884×	body	80	nan
14.0ms	285×	body	80	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	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

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

rewrite43.0ms

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×	`frac-times` `associate-/r*` `associate-/r/` `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 → 114

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
179.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
141.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
73.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify89.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5001	1238

prune362.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
14.0ms	(* (- 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)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
117.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
199.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	744	1044
1	3484	958
2	5001	958

prune280.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Merged error: 0.0b

Counts

116 → 7

localize11.0ms

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))))

rewrite46.0ms

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` `frac-times` `times-frac` `div-exp` `pow-prod-down` `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 → 108

Calls

4 calls:

6.0ms	(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)))))
11.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (- a (/ 1.0 3.0)))
196.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
232.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
88.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	773	1277
1	3999	1177
2	5002	1171

prune256.0ms

Filtered

120 candidates to 85 candidates (70.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	121	6	127

Merged error: 0.0b

Counts

127 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- 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))))
0.5b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
40×	`add-sqr-sqrt`
32×	`frac-times`
26×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-l`
23×	`flip3--` `flip--`
21×	`*-un-lft-identity`
20×	`associate-*r/`
15×	`pow1`
14×	`associate-r`
13×	`add-cube-cbrt`
12×	`flip3-+` `flip-+`
10×	`associate-*l/`
9×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`difference-of-squares` `unswap-sqr`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`cbrt-undiv` `times-frac` `div-exp` `add-log-exp`
3×	`*-commutative` `distribute-lft-out--`
2×	`sqrt-pow1` `pow1/2` `associate-/r/`
1×	`frac-2neg` `sqrt-unprod` `clear-num` `associate-/r` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 148

Calls

4 calls:

14.0ms	(* (sqrt (- 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)))))
14.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
21.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
237.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
88.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
159.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	950	2674
1	4845	2425
2	5002	2425

prune389.0ms

Filtered

160 candidates to 112 candidates (70.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	161	5	166

Merged error: 0b

Counts

166 → 5

regimes74.0ms

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

sample2.1s

Algorithm

intervals

Results

1.2s	27334×	body	80	nan
399.0ms	9118×	body	80	valid

Details

sample88.0ms

simplify95.0ms

prune2.0ms

localize13.0ms

rewrite43.0ms

series515.0ms

simplify89.0ms

prune362.0ms

localize10.0ms

rewrite45.0ms

series436.0ms

simplify80.0ms

prune280.0ms

localize11.0ms

rewrite46.0ms

series557.0ms

simplify100.0ms

prune256.0ms

localize12.0ms

rewrite67.0ms

series716.0ms

simplify122.0ms

prune389.0ms

regimes74.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.1s

Profiling