Details

sample71.0ms

Algorithm

intervals

Results

30.0ms	905×	body	80	nan
10.0ms	284×	body	80	valid

simplify106.0ms

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

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

rewrite183.0ms

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:

50.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
45.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
66.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
66.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
167.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
133.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (79.0ms)

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

prune395.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.4b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
61×	`associate-l`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
34×	`add-cbrt-cube`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-r`
6×	`associate-*l/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 199

Calls

4 calls:

51.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
22.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
57.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
78.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series551.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
74.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
143.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
197.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify52.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1127	2217
1	5001	1992

prune592.0ms

Pruning

7 alts after pruning (5 fresh and 2 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 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
0.2b	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

25.0ms	(sqrt (- a (/ 1.0 3.0)))
92.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
25.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
47.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (- a (/ 1.0 3.0)))
133.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
217.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
82.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify104.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	806	1332
1	4131	1224
2	5001	1220

prune353.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
9.2b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
70×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
44×	`add-cube-cbrt`
39×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`flip3--` `flip--`
5×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-r` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`

Counts

4 → 178

Calls

4 calls:

57.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
22.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
76.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
94.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series506.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
73.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
178.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
111.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify97.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	939	1895
1	3969	1664
2	5003	1637

prune523.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes94.0ms

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

sample1.9s

Algorithm

intervals

Results

815.0ms	26824×	body	80	nan
307.0ms	9113×	body	80	valid