Details

sample129.0ms

Algorithm

intervals

Results

51.0ms	967×	body	80	nan
28.0ms	288×	body	80	valid

simplify1.8s

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))
0.3b	(* (/ 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))))

rewrite258.0ms

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:

68.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
106.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
56.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series826.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
282.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
244.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
86.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.3s

Counts: 126 → 126

prune553.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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

rewrite239.0ms

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:

56.0ms	(* 9.0 (- a (/ 1.0 3.0)))
126.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
32.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 9.0 (- a (/ 1.0 3.0)))
162.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
263.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
89.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.5s

Counts: 109 → 109

prune466.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
5.7b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

25.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
36.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
24.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
165.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series764.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
260.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
104.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
239.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify1.9s

Counts: 109 → 109

prune563.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

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

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
608×	`add-sqr-sqrt`
452×	`sqrt-prod`
440×	`*-un-lft-identity`
346×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`unswap-sqr`
6×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-r` `flip--`
4×	`frac-times` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 525

Calls

4 calls:

18.0ms	(sqrt (- a (/ 1.0 3.0)))
53.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
147.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
45.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (- a (/ 1.0 3.0)))
174.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
236.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
278.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify883.0ms

Counts: 537 → 537

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes86.0ms

Accuracy

-5.3% (0.1b remaining)

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

bsearch0.0ms

simplify1.9s

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.2s	27325×	body	80	nan
1.3s	9148×	body	80	valid