Details

sample73.0ms

Algorithm

intervals

Results

28.0ms	840×	body	80	nan
13.0ms	295×	body	80	valid

simplify101.0ms

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
done	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)))
0.2b	(* (/ 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 (* 9.0 (- a (/ 1.0 3.0))))

rewrite181.0ms

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)))
65.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
43.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
187.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
141.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify94.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (80.0ms)

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

prune402.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)))))))
0.3b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite216.0ms

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:

50.0ms	(* 9.0 (- a (/ 1.0 3.0)))
91.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
22.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
42.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 9.0 (- a (/ 1.0 3.0)))
124.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
205.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
78.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify51.0ms

Counts

195 → 195

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1157	3009
1	5002	2366
done	5002	2366

prune383.0ms

Pruning

6 alts after pruning (6 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)))
0.3b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.8b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite219.0ms

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:

50.0ms	(* 9.0 (- a (/ 1.0 3.0)))
23.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
42.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
95.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 9.0 (- a (/ 1.0 3.0)))
208.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
174.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify120.0ms

Counts

200 → 200

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1106	2987
1	4932	2299
2	5001	2299
done	5001	2299

prune394.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.5b	(* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
7.8b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

rewrite525.0ms

Algorithm

rewrite-expression-head

Rules

78×	`sqrt-pow1`
69×	`pow1`
52×	`sqrt-div`
33×	`add-sqr-sqrt` `associate-*r/`
28×	`sqrt-prod`
25×	`pow-prod-down`
24×	`add-exp-log` `add-cbrt-cube`
20×	`pow1/2` `associate-r`
16×	`flip3--` `*-un-lft-identity` `flip--`
14×	`add-cube-cbrt` `pow-prod-up`
13×	`associate-l`
10×	`frac-times` `prod-exp` `cbrt-unprod`
9×	`swap-sqr`
8×	`associate-/r/` `pow-sqr`
6×	`associate-*l/`
5×	`unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`times-frac` `*-commutative` `difference-of-squares`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `div-inv` `distribute-lft-out--`

Counts

4 → 157

Calls

4 calls:

41.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
42.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
100.0ms	(* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
333.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
98.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
78.0ms	(* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
163.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

simplify104.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	718	1712
1	3701	1442
2	5002	1415
done	5002	1415

prune414.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13
done	19	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

926.0ms	27619×	body	80	nan
338.0ms	9187×	body	80	valid