Details

sample117.0ms

Algorithm

intervals

Results

48.0ms	869×	body	80	nan
18.0ms	289×	body	80	valid

simplify6.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	32	20
2	172	20
3	1144	20
done	5001	20

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)))))

rewrite236.0ms

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)))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
99.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
39.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series809.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
143.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
229.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
260.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify3.4s

Counts

126 → 126

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	303	2615
1	3922	2474
done	5001	2324

prune689.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

64.0ms	(* 9.0 (- a (/ 1.0 3.0)))
153.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
24.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
24.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series701.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 9.0 (- a (/ 1.0 3.0)))
167.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
105.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
361.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify4.6s

Counts

109 → 109

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	264	2121
1	2480	1991
done	5000	1821

prune480.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 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))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite544.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
126×	`add-sqr-sqrt`
102×	`sqrt-prod`
86×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+` `add-log-exp`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 178

Calls

3 calls:

32.0ms	(sqrt (- a (/ 1.0 3.0)))
445.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
46.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series649.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(sqrt (- a (/ 1.0 3.0)))
236.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
362.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify3.9s

Counts

187 → 187

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	367	4605
1	3523	4224
done	5000	4100

prune730.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))))
0.3b	(/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0))))
0.4b	(/ rand (sqrt (cbrt 9.0)))
1.1b	(/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))

rewrite9.4s

Algorithm

rewrite-expression-head

Rules

17974×	`times-frac`
9342×	`add-sqr-sqrt`
7662×	`*-un-lft-identity`
7167×	`sqrt-prod`
6540×	`add-cube-cbrt`
1479×	`cbrt-prod`
1120×	`difference-of-squares`
560×	`distribute-lft-out--`
468×	`div-inv`
324×	`associate-/r*`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/l*`
19×	`cbrt-undiv` `div-exp` `associate-/r/`
6×	`pow1` `associate-l`
4×	`frac-times` `flip3--` `associate-r` `flip--` `add-log-exp`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
2×	`sqrt-div` `associate-r/` `associate-l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 5287

Calls

4 calls:

7.8s	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))))
56.0ms	(/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0))))
8.0ms	(/ rand (sqrt (cbrt 9.0)))
260.0ms	(/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

238.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))))
445.0ms	(/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0))))
141.0ms	(/ rand (sqrt (cbrt 9.0)))
305.0ms	(/ (/ 1.0 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (/ (sqrt (- a (/ 1.0 3.0))) (/ rand (sqrt (cbrt 9.0)))))

simplify4.1s

Counts

5299 → 5299

Iterations

Useful iterations: 0 (1.4s)

Iter	Nodes	Cost
0	5798	247862
done	5798	247862

prune39.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes115.0ms

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	13	20
1	17	20
done	17	20

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.7s	26942×	body	80	nan
890.0ms	9096×	body	80	valid