Details

analyze76.0ms

Algorithm: search

sample26.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
0.0ms	8×	body	80	nan
0.0ms	6×	body	80	invalid

simplify94.0ms

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: 0.2b

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

series50.0ms

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)))
19.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify102.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4617	1341
2	5001	1341

prune534.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

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)))))
0.4b	(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)))
13.0ms	(* (- 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))))

series39.0ms

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)))))))
17.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(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

prune240.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	110	6	116

Merged error: 0.0b

Counts

116 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.2b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
15×	`*-un-lft-identity`
11×	`pow1` `add-cube-cbrt`
10×	`times-frac`
9×	`associate-r/` `associate-l*`
6×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l/` `-commutative` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 102

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify88.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	857	1103
1	4190	994
2	5002	994

prune239.0ms

Filtered

86 candidates to 114 candidates (-32.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	115	5	120

Merged error: 0b

Counts

120 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
127×	`add-sqr-sqrt`
102×	`sqrt-prod`
89×	`*-un-lft-identity`
59×	`add-cube-cbrt`
26×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `flip3-+` `sqrt-div` `associate-r` `flip-+`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

28.0ms	(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (- a (/ 1.0 3.0)))
33.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
16.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
3.0ms	(sqrt (- a (/ 1.0 3.0)))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
18.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1142	2786
1	5001	2617

prune414.0ms

Filtered

132 candidates to 202 candidates (-53.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	202	5	207

Merged error: 0b

Counts

207 → 5

regimes189.0ms

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	11
1	17	11

end0.0ms

analyze78.0ms

Algorithm: search

sample648.0ms

Algorithm

intervals

Results

475.0ms	8000×	body	80	valid
15.0ms	272×	body	80	nan
14.0ms	244×	body	80	invalid

Details

analyze76.0ms

sample26.0ms

simplify94.0ms

prune3.0ms

localize10.0ms

rewrite43.0ms

series50.0ms

simplify102.0ms

prune534.0ms

localize10.0ms

rewrite45.0ms

series39.0ms

simplify89.0ms

prune240.0ms

localize13.0ms

rewrite49.0ms

series46.0ms

simplify88.0ms

prune239.0ms

localize11.0ms

rewrite91.0ms

series53.0ms

simplify49.0ms

prune414.0ms

regimes189.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze78.0ms

sample648.0ms

Profiling