Details

sample141.0ms

Algorithm

intervals

Results

68.0ms	869×	body	80	nan
19.0ms	289×	body	80	valid

simplify10.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	188	20
4	417	20
5	772	20
6	1496	20
7	2490	20
8	3402	20
9	4724	20
done	5000	20

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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

rewrite214.0ms

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×	`frac-times` `associate-/r*` `associate-/r/` `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 → 114

Calls

4 calls:

73.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
88.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
24.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
102.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
268.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
225.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.2s

Counts

126 → 126

Iterations

Useful iterations: 2 (835.0ms)

Iter	Nodes	Cost
0	303	2615
1	823	2480
2	2960	2274
done	5002	2274

prune595.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

59.0ms	(* 9.0 (- a (/ 1.0 3.0)))
60.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
13.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 9.0 (- a (/ 1.0 3.0)))
161.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
101.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
272.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.5s

Counts

116 → 116

Iterations

Useful iterations: 2 (449.0ms)

Iter	Nodes	Cost
0	271	2223
1	723	2134
2	2620	1938
done	5002	1938

prune517.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
1.1b	(/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

83.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)))))
15.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
33.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
69.0ms	(/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series798.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)))))
121.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
241.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
267.0ms	(/ 1 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify2.0s

Counts

177 → 177

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	388	4041
1	1005	3699
2	3181	3258
done	5001	3226

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

183×	`add-sqr-sqrt`
175×	`sqrt-prod`
162×	`times-frac`
125×	`*-un-lft-identity`
106×	`associate-l`
97×	`add-cube-cbrt`
34×	`add-exp-log` `add-cbrt-cube`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
13×	`pow1` `prod-exp` `cbrt-unprod`
9×	`associate-/r*`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l/` `associate-/l` `unswap-sqr`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `sqrt-undiv` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 263

Calls

4 calls:

96.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
121.0ms	(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
49.0ms	(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
175.0ms	(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

series1.2s

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
268.0ms	(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
128.0ms	(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
459.0ms	(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

simplify2.7s

Counts

275 → 275

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	436	5863
1	1170	5477
2	4746	4811
done	5001	4787

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	21	22
done	21	22

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.3s	26942×	body	80	nan
1.2s	9096×	body	80	valid