Details

sample69.0ms

Algorithm

intervals

Results

28.0ms	869×	body	80	nan
14.0ms	297×	body	80	valid

simplify104.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

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)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))

rewrite121.0ms

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:

32.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
34.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
41.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
280.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
202.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
153.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1278

prune422.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt` `prod-diff`
60×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-r`
9×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`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` `distribute-lft-out` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

34.0ms	(* 9.0 (- a (/ 1.0 3.0)))
55.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
36.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
131.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
211.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune408.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.5b	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

67×	`pow1`
41×	`pow-prod-down`
40×	`add-sqr-sqrt`
36×	`sqrt-div`
32×	`associate-*r/`
28×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
20×	`sqrt-pow1` `pow1/2`
19×	`associate-r`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt` `flip3--` `flip--`
13×	`associate-l`
11×	`prod-exp` `cbrt-unprod`
8×	`frac-times` `associate-/r/` `pow-prod-up` `unswap-sqr`
7×	`sqrt-unprod`
6×	`times-frac` `pow-sqr`
4×	`expm1-log1p-u` `associate-l/` `associate-/r` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`*-commutative`
2×	`cbrt-undiv` `pow-plus` `div-exp` `distribute-lft-out--`
1×	`pow2` `frac-2neg` `swap-sqr` `clear-num` `rem-square-sqrt` `div-inv` `associate-/l*`

Counts

4 → 161

Calls

4 calls:

73.0ms	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
29.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
32.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
71.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
95.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
97.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
106.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	678	1632
1	3199	1433
2	5001	1383

prune477.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `frac-times`
27×	`*-un-lft-identity`
25×	`times-frac`
23×	`add-cube-cbrt` `associate-l`
20×	`associate-*r/`
18×	`flip3-+` `flip-+`
16×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`flip3--` `flip--`
10×	`sqrt-prod`
9×	`associate-*l/`
6×	`sqrt-div`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num`

Counts

4 → 141

Calls

4 calls:

33.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
40.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
96.0ms	(* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))

series1.1s

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
230.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
149.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
637.0ms	(* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))

simplify45.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1274	2457
1	5001	2112

prune660.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes95.0ms

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	20	18
1	20	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

853.0ms	27184×	body	80	nan
321.0ms	9100×	body	80	valid