Details

sample188.0ms

Algorithm

intervals

Results

123.0ms	926×	body	80	nan
34.0ms	306×	body	80	valid

simplify662.0ms

Calls

1 calls:

Slowest

662.0ms

(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b	(* 9 (- a (/ 1.0 3.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `flip--`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-/r/` `sqrt-prod`
1×	`clear-num` `frac-2neg` `pow1/2` `*-commutative` `fma-udef` `div-inv`

Calls

4 calls:

Slowest

2.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
2.0ms	(* 9 (- a (/ 1.0 3.0)))
1.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series136.0ms

Calls

4 calls:

Slowest

56.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
40.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
23.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
17.0ms	(* 9 (- a (/ 1.0 3.0)))

simplify1.8s

Calls

30 calls:

Slowest

321.0ms	(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
200.0ms	(- (* 1/3 (* (sqrt -3.0) rand)) (+ (* 4.5 (/ (* (pow a 2) rand) (sqrt -3.0))) (+ (* 1.5 (/ (* a rand) (sqrt -3.0))) (* 3.375 (/ (* (pow a 2) rand) (pow (sqrt -3.0) 3))))))
187.0ms	(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
149.0ms	(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
119.0ms	(+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))

prune701.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.0b	(+ (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`flip3--` `flip--`
12×	`associate-*r/`
10×	`frac-add`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`frac-times` `pow1` `add-cbrt-cube` `sqrt-div` `associate-l` `add-exp-log` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `expm1-log1p-u` `associate-+l+` `associate-/r*` `distribute-lft-in` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `associate-*l/`
2×	`associate-+r+` `sqrt-prod` `div-inv`
1×	`+-commutative` `clear-num` `associate-+r-` `sum-log` `fma-def` `frac-2neg` `distribute-lft1-in` `flip3-+` `distribute-rgt-out` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

15.0ms	(+ (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
13.0ms	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
4.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
2.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series200.0ms

Calls

4 calls:

Slowest

63.0ms	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
60.0ms	(+ (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
52.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
24.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.4s

Calls

74 calls:

Slowest

509.0ms	(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
501.0ms	(+ (* (* rand (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
438.0ms	(+ (* (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (+ a (/ 1.0 3.0)) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
425.0ms	(* (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))) (+ a (/ 1.0 3.0)))
420.0ms	(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

8.3b	(* a (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b	(* (- (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-r` `associate-l`
10×	`associate-*r/`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `div-inv` `flip--` `add-log-exp`
2×	`pow1/2` `*-commutative` `sqrt-prod` `distribute-neg-frac`
1×	`distribute-lft-neg-out` `frac-times` `neg-mul-1` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`

Calls

4 calls:

Slowest

6.0ms	(* (- (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
2.0ms	(* a (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
2.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
2.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series237.0ms

Calls

4 calls:

Slowest

125.0ms	(* a (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
64.0ms	(* (- (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
27.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify4.4s

Calls

47 calls:

Slowest

426.0ms	(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
361.0ms	(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
254.0ms	(* (- (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
229.0ms	(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
218.0ms	(- (* 1/3 (* a (* (sqrt -3.0) rand))) (+ (* 3.375 (/ (* (pow a 3) rand) (pow (sqrt -3.0) 3))) (+ (* 4.5 (/ (* (pow a 3) rand) (sqrt -3.0))) (* 1.5 (/ (* (pow a 2) rand) (sqrt -3.0))))))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
0.3b	(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.0b	(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
0.0b	(sqrt (- a (/ 1.0 3.0)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
39×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-l` `sqrt-prod`
15×	`div-inv`
14×	`flip3--` `flip--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`frac-add`
6×	`frac-times` `pow1` `associate-/r` `sqrt-div` `associate-r/` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `expm1-log1p-u` `associate-+l+` `distribute-lft-in` `associate-/r/` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `associate-*l/`
2×	`cbrt-undiv` `associate-+r+` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `fma-def` `frac-2neg` `distribute-lft1-in` `flip3-+` `distribute-rgt-out` `pow1/2` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/`

Calls

4 calls:

Slowest

25.0ms	(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
19.0ms	(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
9.0ms	(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
2.0ms	(sqrt (- a (/ 1.0 3.0)))

series189.0ms

Calls

4 calls:

Slowest

57.0ms	(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
57.0ms	(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
47.0ms	(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
27.0ms	(sqrt (- a (/ 1.0 3.0)))

simplify17.7s

Calls

158 calls:

Slowest

555.0ms	(+ (* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (+ a (/ 1.0 3.0)) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
539.0ms	(+ (* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
538.0ms	(* (exp (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))) (exp (- a (/ 1.0 3.0))))
495.0ms	(+ (* (* (/ rand (sqrt 9)) (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (* (sqrt (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
475.0ms	(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.8s	27982×	body	80	nan
1.3s	9187×	body	80	valid