Details

sample129.0ms

Algorithm

intervals

Results

70.0ms	936×	body	80	nan
29.0ms	292×	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: 0.1b

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)))))

rewrite115.0ms

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	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
32.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
39.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
183.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
150.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (78.0ms)

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

prune403.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))))
9.9b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite195.0ms

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:

34.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
37.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
112.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series582.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
188.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
151.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
167.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify77.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	787	1286
1	3151	1135
2	5001	1129

prune391.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize11.0ms

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))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.9b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
79×	`add-cube-cbrt`
78×	`prod-diff`
64×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
9×	`associate-r/` `associate-l*`
8×	`div-inv`
6×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`frac-times` `sub-neg` `sqrt-pow1` `associate-l/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 188

Calls

4 calls:

34.0ms	(* 9.0 (- a (/ 1.0 3.0)))
32.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
13.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
52.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 9.0 (- a (/ 1.0 3.0)))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
196.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
167.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1106	2989
1	4926	2299
2	5001	2299

prune588.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(* (* (- a (/ 1.0 3.0)) (/ 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	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite217.0ms

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:

33.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
118.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
53.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
210.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
155.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
132.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	758	1394
1	3358	1232
2	5002	1226

prune364.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes63.0ms

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	13
1	19	13

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	27843×	body	80	nan
833.0ms	9136×	body	80	valid