Details

analyze80.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample24.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	11×	body	80	invalid
0.0ms	8×	body	80	nan

simplify148.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune11.0ms

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 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
0.3b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.4b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
12×	`associate-l`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`sqrt-pow1` `associate-r/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (- a (/ 1.0 3.0)) 9.0)
23.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
10.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (- a (/ 1.0 3.0)) 9.0)
13.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) 1))
18.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5787	1905

prune307.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* a 9.0) 3.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (- (* a 9.0) 3.0))) 1))
0.3b	(/ rand (sqrt (- (* a 9.0) 3.0)))
0.4b	(sqrt (- (* a 9.0) 3.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`times-frac`
15×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`flip3--` `associate-l` `associate-/r*` `flip--` `add-log-exp`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`associate-r/` `associate-l/` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

4.0ms	(- (* a 9.0) 3.0)
20.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (- (* a 9.0) 3.0))) 1))
6.0ms	(/ rand (sqrt (- (* a 9.0) 3.0)))
4.0ms	(sqrt (- (* a 9.0) 3.0))

series31.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (* a 9.0) 3.0)
11.0ms	(* (- a (/ 1.0 3.0)) (+ (/ rand (sqrt (- (* a 9.0) 3.0))) 1))
13.0ms	(/ rand (sqrt (- (* a 9.0) 3.0)))
4.0ms	(sqrt (- (* a 9.0) 3.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5098	1758

prune271.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Merged error: 0.0b

Counts

119 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.2b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
261×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate-r` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 355

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
71.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
18.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series45.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) 1))
11.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
17.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

367 → 367

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4988	7942
1	4988	7942

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	364	3	367
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	367	8	375

Merged error: 0b

Counts

375 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
52×	`add-exp-log`
34×	`add-cbrt-cube`
28×	`associate-l`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac` `prod-exp` `sqrt-prod`
16×	`div-exp`
12×	`pow1`
11×	`cbrt-unprod`
10×	`unswap-sqr`
9×	`cbrt-undiv` `associate-*l/`
6×	`flip3--` `sqrt-div` `flip--`
5×	`cbrt-prod` `frac-times` `pow-prod-down`
4×	`associate-/r/` `add-log-exp` `difference-of-squares`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `distribute-lft-out--`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `clear-num` `associate-/r*`

Counts

4 → 149

Calls

4 calls:

25.0ms	(* (- a (/ 1.0 3.0)) (+ (* (/ 1 (fabs (cbrt 9.0))) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0))))) 1))
12.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0))))
18.0ms	(* (/ 1 (fabs (cbrt 9.0))) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0)))))
13.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (- a (/ 1.0 3.0)) (+ (* (/ 1 (fabs (cbrt 9.0))) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0))))) 1))
21.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0))))
29.0ms	(* (/ 1 (fabs (cbrt 9.0))) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0)))))
8.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt (cbrt 9.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5012	3475

prune734.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	161	8	169

Merged error: 0b

Counts

169 → 8

regimes240.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	44	18
1	44	18

end0.0ms

sample635.0ms

Algorithm

intervals

Results

465.0ms	8000×	body	80	valid
14.0ms	272×	body	80	nan
14.0ms	250×	body	80	invalid

Details

analyze80.0ms

sample24.0ms

simplify148.0ms

prune11.0ms

localize13.0ms

rewrite52.0ms

series40.0ms

simplify35.0ms

prune307.0ms

localize14.0ms

rewrite37.0ms

series31.0ms

simplify35.0ms

prune271.0ms

localize14.0ms

rewrite132.0ms

series45.0ms

simplify93.0ms

prune1.5s

localize20.0ms

rewrite77.0ms

series84.0ms

simplify50.0ms

prune734.0ms

regimes240.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample635.0ms

Profiling