Details

sample67.0ms

Algorithm

intervals

Results

30.0ms	930×	body	80	nan
11.0ms	296×	body	80	valid

simplify102.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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:

31.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
31.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
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)))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
133.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
149.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (80.0ms)

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

prune424.0ms

Pruning

9 alts after pruning (9 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	(sqrt (* 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)))))

rewrite133.0ms

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:

32.0ms	(* 9.0 (- a (/ 1.0 3.0)))
31.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
51.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
10.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
132.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
198.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune451.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
93×	`times-frac`
72×	`*-un-lft-identity`
63×	`sqrt-prod`
54×	`add-cube-cbrt`
36×	`associate-r`
28×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`difference-of-squares`
10×	`unswap-sqr`
9×	`pow1` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `flip--`
5×	`cbrt-undiv` `frac-times` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r/` `associate-l/` `flip-+` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 194

Calls

4 calls:

16.0ms	(sqrt (- a (/ 1.0 3.0)))
28.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
13.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
51.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (- a (/ 1.0 3.0)))
154.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
95.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
247.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1070	2187
1	4955	2047
2	5001	2047

prune639.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

227×	`add-sqr-sqrt`
180×	`times-frac`
110×	`*-un-lft-identity`
99×	`associate-r` `sqrt-prod`
92×	`add-cube-cbrt`
66×	`associate-l`
40×	`add-exp-log` `add-cbrt-cube`
27×	`unswap-sqr`
18×	`difference-of-squares`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
10×	`pow1`
9×	`distribute-lft-out--`
6×	`sqrt-div` `associate-/r/` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `frac-times` `flip3--` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 273

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
50.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))
51.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))
48.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

441.0ms	(cbrt (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
243.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))
240.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))
244.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	816	3099
1	3315	2931
2	5001	2882

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes247.0ms

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	10
1	17	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

893.0ms	27188×	body	80	nan
332.0ms	9148×	body	80	valid