Details

analyze85.0ms

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

sample25.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
1.0ms	13×	body	80	nan
1.0ms	11×	body	80	invalid

simplify147.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune11.0ms

Filtered

1 candidates to 1 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: 0.2b

Counts

2 → 2

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

rewrite48.0ms

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:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4974	2418
1	4974	2418

prune356.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Merged error: 0.0b

Counts

128 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.4b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite55.0ms

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×	`associate-r` `associate-/r*` `associate-/r/` `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 → 111

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
7.0ms	(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))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify39.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5182	2263

prune336.0ms

Filtered

105 candidates to 123 candidates (-17.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	125	7	132

Merged error: 0b

Counts

132 → 7

localize12.0ms

Local error

Found 4 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)))))
0.2b	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
13.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
14.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
12.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
10.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
22.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
7.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4980	2507
1	4980	2507

prune305.0ms

Filtered

96 candidates to 130 candidates (-35.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Merged error: 0b

Counts

137 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))))
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.2b	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
37×	`associate-r`
34×	`add-cbrt-cube`
31×	`associate-l`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv`
6×	`associate-*r/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-l/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 191

Calls

4 calls:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))))
11.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
16.0ms	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
18.0ms	(* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))))
6.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
12.0ms	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
19.0ms	(* (/ 1 (sqrt 9.0)) (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5016	3516

prune508.0ms

Filtered

140 candidates to 203 candidates (-45.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	203	7	210

Merged error: 0b

Counts

210 → 7

regimes257.0ms

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	35	21
1	35	21

end0.0ms

sample670.0ms

Algorithm

intervals

Results

496.0ms	8000×	body	80	valid
15.0ms	253×	body	80	invalid
15.0ms	266×	body	80	nan

Details

analyze85.0ms

sample25.0ms

simplify147.0ms

prune11.0ms

localize11.0ms

rewrite48.0ms

series51.0ms

simplify53.0ms

prune356.0ms

localize12.0ms

rewrite55.0ms

series52.0ms

simplify39.0ms

prune336.0ms

localize12.0ms

rewrite53.0ms

series56.0ms

simplify53.0ms

prune305.0ms

localize13.0ms

rewrite64.0ms

series54.0ms

simplify50.0ms

prune508.0ms

regimes257.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample670.0ms

Profiling