Details

sample81.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 74.609375%

Guaranteed chance to sample good point: 98.461538%

Results

14.0ms	256×	body	80	valid
2.0ms	37×	body	80	invalid
0.0ms	3×	body	80	nan

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

prune3.0ms

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

rewrite49.0ms

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
20.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify107.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4619	1341
2	5001	1341

prune334.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	0	1	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)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite44.0ms

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)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 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)))))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
18.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	870	1101
1	4263	1027
2	5001	1027

prune228.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
606×	`add-sqr-sqrt`
446×	`sqrt-prod`
439×	`*-un-lft-identity`
345×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `flip--` `add-log-exp`
4×	`frac-times` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 522

Calls

4 calls:

6.0ms	(- a (/ 1.0 3.0))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
44.0ms	(* (/ (/ 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))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- a (/ 1.0 3.0))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
28.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
11.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify99.0ms

Algorithm

egg-herbie

Counts

534 → 534

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1779	6732
1	5001	6480

prune1.7s

Filtered

322 candidates to 534 candidates (-65.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	533	1	534
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	536	6	542

Merged error: 0.0b

Counts

542 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))) rand)
0.4b	(/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
1.0b	(/ 1.0 (sqrt (cbrt 9.0)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

1178×	`times-frac`
864×	`add-sqr-sqrt`
752×	`sqrt-prod`
643×	`*-un-lft-identity`
517×	`add-cube-cbrt`
288×	`associate-r`
259×	`add-exp-log`
185×	`cbrt-prod`
127×	`prod-exp`
126×	`difference-of-squares`
100×	`div-exp`
94×	`add-cbrt-cube`
63×	`distribute-lft-out--`
36×	`1-exp`
34×	`cbrt-undiv` `cbrt-unprod` `associate-/l*`
23×	`div-inv`
18×	`rec-exp` `associate-/r*`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-l`
5×	`associate-*l/`
4×	`sqrt-div` `pow-prod-down` `associate-/r/` `add-log-exp`
2×	`frac-times` `flip3--` `frac-2neg` `associate-r/` `clear-num` `-commutative` `flip--`
1×	`associate-/l/`

Counts

4 → 797

Calls

4 calls:

91.0ms	(* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0)))))
69.0ms	(* (* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))) rand)
32.0ms	(/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
5.0ms	(/ 1.0 (sqrt (cbrt 9.0)))

series79.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0)))))
42.0ms	(* (* (/ 1 (* 1 (fabs (cbrt 9.0)))) (/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))) rand)
14.0ms	(/ (/ 1.0 (sqrt (cbrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
0.0ms	(/ 1.0 (sqrt (cbrt 9.0)))

simplify161.0ms

Algorithm

egg-herbie

Counts

807 → 807

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	3196	12639
1	5002	11628

prune3.1s

Filtered

424 candidates to 807 candidates (-90.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	807	0	807
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	807	6	813

Merged error: 0.0b

Counts

813 → 6

regimes157.0ms

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

sample823.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 74.609375%

Guaranteed chance to sample good point: 98.461538%

Results

470.0ms	8000×	body	80	valid
62.0ms	1095×	body	80	invalid
6.0ms	121×	body	80	nan

Details

sample81.0ms

simplify95.0ms

prune3.0ms

localize10.0ms

rewrite49.0ms

series49.0ms

simplify107.0ms

prune334.0ms

localize10.0ms

rewrite44.0ms

series41.0ms

simplify89.0ms

prune228.0ms

localize11.0ms

rewrite121.0ms

series56.0ms

simplify99.0ms

prune1.7s

localize17.0ms

rewrite274.0ms

series79.0ms

simplify161.0ms

prune3.1s

regimes157.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample823.0ms

Profiling