Details

sample72.0ms

Algorithm

intervals

Results

27.0ms	926×	body	80	nan
13.0ms	299×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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

rewrite170.0ms

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:

48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
39.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
17.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
62.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

series517.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
145.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
179.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify91.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	860	1391
1	3770	1282
2	5002	1276

prune408.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))))

rewrite205.0ms

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:

47.0ms	(* 9.0 (- a (/ 1.0 3.0)))
87.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
42.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
20.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 9.0 (- a (/ 1.0 3.0)))
125.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
68.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
200.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1157	3009
1	5002	2366

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))
0.2b	(/ (* 1.0 rand) (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
0.4b	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

234×	`prod-diff`
222×	`add-sqr-sqrt`
215×	`*-un-lft-identity`
213×	`add-cube-cbrt`
205×	`distribute-rgt-in` `distribute-lft-in`
167×	`times-frac`
31×	`pow1`
23×	`add-exp-log`
19×	`div-inv`
17×	`pow-prod-down`
16×	`add-cbrt-cube`
14×	`associate-*r/`
10×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`sub-neg`
5×	`sqrt-pow1`
4×	`cbrt-prod` `expm1-log1p-u` `flip3--` `sqrt-div` `associate-/r*` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*` `distribute-lft-out--`

Counts

4 → 346

Calls

4 calls:

48.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
122.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))
62.0ms	(/ (* 1.0 rand) (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
88.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
82.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))
211.0ms	(/ (* 1.0 rand) (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
122.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))

simplify97.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1921	8704
1	5001	7002

prune530.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

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	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
1.1b	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac`
71×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
64×	`add-cube-cbrt`
19×	`associate-/r*`
17×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`associate-/l*`
6×	`associate-r/` `associate-l*` `div-inv`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `sqrt-div` `div-exp` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `sqrt-pow1` `pow-prod-down` `associate-*l/` `clear-num` `associate-/l/` `difference-of-squares`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 168

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))))
38.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
18.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series507.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))))
70.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
140.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
180.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify117.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1075	2095
1	4845	1980
2	5001	1980

prune519.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes78.0ms

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	21	15
1	21	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

791.0ms	26636×	body	80	nan
299.0ms	9118×	body	80	valid