Details

sample98.0ms

Algorithm

intervals

Results

51.0ms	709×	body	80	nan
21.0ms	295×	body	80	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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

rewrite107.0ms

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×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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 → 122

Calls

4 calls:

27.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
35.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
30.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series45.0ms

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)))
17.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
8.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.4b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite180.0ms

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×	`expm1-log1p-u` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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 → 119

Calls

4 calls:

36.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
29.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
102.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series45.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
8.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
16.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify79.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	787	1284
1	3157	1135
2	5001	1129

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`associate-*l/`
8×	`associate-*r/` `sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 123

Calls

4 calls:

107.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
48.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
30.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
7.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
8.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
5.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	758	1396
1	3352	1232
2	5001	1226

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.2b	(* (* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
0.4b	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
605×	`add-sqr-sqrt`
452×	`sqrt-prod`
439×	`*-un-lft-identity`
345×	`add-cube-cbrt`
207×	`associate-r`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
32×	`add-exp-log` `add-cbrt-cube`
22×	`associate-/l*`
21×	`div-inv`
12×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r`
7×	`flip3--` `associate-l` `flip--` `unswap-sqr`
6×	`sqrt-div`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 536

Calls

4 calls:

15.0ms	(sqrt (- a (/ 1.0 3.0)))
107.0ms	(* (* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))) rand)
108.0ms	(* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
23.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (- a (/ 1.0 3.0)))
24.0ms	(* (* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))) rand)
9.0ms	(* (- a (/ 1.0 3.0)) (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
10.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify93.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1744	7278
1	5002	6816

prune4.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes266.0ms

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	19	14
1	19	14

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.0s	27759×	body	80	nan
680.0ms	9179×	body	80	valid