Details

Time bar (total: 1.1m)

sample226.0ms

Algorithm
intervals
Results
149.0ms926×body80nan
41.0ms306×body80valid

simplify223.0ms

Calls
1 calls:
Slowest
222.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×associate-*r*
9×associate-*r/
8×sqrt-prod
6×add-cbrt-cube sqrt-div add-exp-log
5×flip3-- flip--
4×pow1 associate-/r* associate-/r/ insert-posit16 add-log-exp
3×associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-sub div-exp
Calls
4 calls:
Slowest
11.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
7.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
4.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series141.0ms

Calls
4 calls:
Slowest
53.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
33.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
27.0ms
(* 9 (- a (/ 1.0 3.0)))
26.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify6.5s

Calls
80 calls:
Slowest
523.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
345.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
235.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
209.0ms
(- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))
209.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
0.3b
(* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
0.2b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-div
33×associate-*r/
30×associate-*r*
25×flip3-- flip--
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×frac-times associate-/r/
11×sqrt-prod
8×add-cbrt-cube associate-*l/ add-exp-log
6×pow1
4×associate-/r* insert-posit16 add-log-exp
3×associate-/l*
2×*-commutative div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-sub div-exp associate-*l* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
15.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
9.0ms
(* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
8.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))))
6.0ms
(sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))

series158.0ms

Calls
4 calls:
Slowest
53.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))))
42.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
35.0ms
(* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
28.0ms
(sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))

simplify12.5s

Calls
110 calls:
Slowest
759.0ms
(* (* (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (* 9 (sqrt (- a (/ 1.0 3.0))))) (* 9 (sqrt (- a (/ 1.0 3.0))))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
416.0ms
(sqrt (* (* 9 (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))) (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
413.0ms
(sqrt (* (* 9 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))))
406.0ms
(sqrt (* (* 9 (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))) (sqrt (- a (/ 1.0 3.0)))))
390.0ms
(* (* 9 (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))) (sqrt (- a (/ 1.0 3.0))))

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.2b
(* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))
0.0b
(/ (- a (/ 1.0 3.0)) (sqrt 9))
0.0b
(+ (* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
282×times-frac
158×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
84×associate-*r*
81×sqrt-prod
16×div-inv associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r*
6×add-log-exp
4×pow1 cbrt-undiv flip3-- sqrt-div div-exp associate-/r/ insert-posit16 flip--
3×div-sub associate-*r/ associate-/l/
2×associate-+r+ clear-num frac-2neg frac-add
1×+-commutative associate-+r- sum-log sub-neg flip3-+ *-commutative flip-+
Calls
4 calls:
Slowest
15.0ms
(/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
11.0ms
(+ (* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
8.0ms
(* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))
6.0ms
(/ (- a (/ 1.0 3.0)) (sqrt 9))

series166.0ms

Calls
4 calls:
Slowest
50.0ms
(* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))
49.0ms
(+ (* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
43.0ms
(/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
23.0ms
(/ (- a (/ 1.0 3.0)) (sqrt 9))

simplify24.4s

Calls
315 calls:
Slowest
494.0ms
(- (- (log (- a (/ 1.0 3.0))) (log (sqrt 9))) (log (sqrt (- a (/ 1.0 3.0)))))
444.0ms
(/ (/ (* (cbrt (- a (/ 1.0 3.0))) (cbrt (- a (/ 1.0 3.0)))) (* (cbrt (sqrt 9)) (cbrt (sqrt 9)))) (* (cbrt (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt (- a (/ 1.0 3.0))))))
426.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
326.0ms
(* (sqrt (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
315.0ms
(* (exp (* rand (/ (/ (- a (/ 1.0 3.0)) (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))) (exp (- a (/ 1.0 3.0))))

prune3.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0))))
0.3b
(* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3))
0.3b
(/ (sqrt (- a (/ 1.0 3.0))) 3)
0.2b
(* rand (/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
15×sqrt-prod
14×sqrt-div
12×times-frac
11×add-cbrt-cube add-exp-log
7×flip3-- flip-- associate-/l* associate-/l/
6×pow1 associate-/r* associate-*l*
4×frac-times associate-*l/ associate-/r/ insert-posit16 div-inv add-log-exp
3×associate-*r/
2×cbrt-undiv clear-num frac-2neg div-exp prod-exp *-commutative cbrt-unprod
1×pow-prod-down
Calls
4 calls:
Slowest
17.0ms
(/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0))))
7.0ms
(* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3))
3.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
3.0ms
(* rand (/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0)))))

series173.0ms

Calls
4 calls:
Slowest
62.0ms
(* rand (/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0)))))
41.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
39.0ms
(/ (* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (sqrt (- a (/ 1.0 3.0))))
31.0ms
(* (sqrt (- a (/ 1.0 3.0))) (/ (sqrt (- a (/ 1.0 3.0))) 3))

simplify8.8s

Calls
80 calls:
Slowest
722.0ms
(- (+ (log (sqrt (- a (/ 1.0 3.0)))) (log (/ (sqrt (- a (/ 1.0 3.0))) 3))) (log (sqrt (- a (/ 1.0 3.0)))))
461.0ms
(* (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3))) (/ (sqrt (- a (/ 1.0 3.0))) 3))
458.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
403.0ms
(* (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3))) (sqrt (- a (/ 1.0 3.0))))
398.0ms
(* (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3))) (/ (sqrt (- a (/ 1.0 3.0))) 3))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.8s27982×body80nan
1.3s9187×body80valid