Details

sample103.0ms

Algorithm

intervals

Results

53.0ms	922×	body	80	nan
16.0ms	300×	body	80	valid

simplify98.0ms

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

rewrite50.0ms

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:

13.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
15.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
20.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify112.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (23.0ms)

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

prune377.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

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

rewrite47.0ms

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

series40.0ms

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

simplify91.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (19.0ms)

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

prune254.0ms

Filtered

83 candidates to 109 candidates (-31.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	109	9	118

Merged error: 0.0b

Counts

118 → 9

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))))

rewrite49.0ms

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:

8.0ms	(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)))))))
13.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
12.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- a (/ 1.0 3.0)))
16.0ms	(* (- 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)))))
7.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify115.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	923	1353
1	4906	1269
2	5002	1269

prune294.0ms

Filtered

89 candidates to 120 candidates (-34.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	121	8	129

Merged error: 0b

Counts

129 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

27×	`sqrt-prod`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`associate-l`
15×	`pow1`
12×	`sqrt-div`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-*r/`
5×	`pow-prod-down`
4×	`flip3--` `sqrt-pow1` `associate-/r*` `associate-/r/` `flip--` `add-log-exp`
3×	`associate-l/` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`pow1/2` `div-inv`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `div-exp` `associate-r` `clear-num` `*-commutative`

Counts

4 → 98

Calls

4 calls:

11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
26.0ms	(* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (* (sqrt (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	794	1316
1	3551	1202
2	5003	1202

prune379.0ms

Filtered

94 candidates to 110 candidates (-17.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Merged error: 0b

Counts

118 → 8

regimes184.0ms

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	18	11
1	18	11

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	27124×	body	80	nan
514.0ms	9144×	body	80	valid

Details

sample103.0ms

simplify98.0ms

prune3.0ms

localize10.0ms

rewrite50.0ms

series51.0ms

simplify112.0ms

prune377.0ms

localize10.0ms

rewrite47.0ms

series40.0ms

simplify91.0ms

prune254.0ms

localize11.0ms

rewrite49.0ms

series44.0ms

simplify115.0ms

prune294.0ms

localize13.0ms

rewrite58.0ms

series54.0ms

simplify78.0ms

prune379.0ms

regimes184.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

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