Details

Time bar (total: 23.0s)

sample199.0ms

Algorithm
intervals
Results
135.0ms957×body80nan
35.0ms286×body80valid

simplify287.0ms

Calls
1 calls:
Slowest
287.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

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

series182.0ms

Calls
4 calls:
Slowest
65.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
57.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
42.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
18.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify2.0s

Calls
30 calls:
Slowest
390.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
284.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
159.0ms
(- (* 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))))))
150.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
114.0ms
(sqrt (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune684.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
0.2b
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u associate-/r* add-cbrt-cube sqrt-div associate-*r/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×div-inv
2×clear-num frac-2neg flip3-- sqrt-prod flip-- associate-/l/
1×rec-exp pow1/2 associate-/r/ fma-udef pow-flip inv-pow
Calls
4 calls:
Slowest
3.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
2.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
1.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
0.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series215.0ms

Calls
4 calls:
Slowest
85.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
65.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
42.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
24.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify2.6s

Calls
25 calls:
Slowest
540.0ms
(- (+ (* 3/2 (/ a (* (sqrt (- 0.3333333333333333)) rand))) (* 3 (/ (sqrt (- 0.3333333333333333)) rand))) (* 3/8 (/ (pow a 2) (* (pow (sqrt (- 0.3333333333333333)) 3) rand))))
385.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
371.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
223.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
184.0ms
(- a (+ (* 0.1111111111111111 (* (sqrt -3.0) rand)) 0.3333333333333333))

prune663.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (/ (/ 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)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×sqrt-prod
8×div-inv
6×associate-/r*
5×add-cbrt-cube add-exp-log
4×sqrt-div associate-/l*
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×flip3-- associate-/r/ flip--
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg pow1/2 div-exp fma-udef associate-/l/
Calls
3 calls:
Slowest
10.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
2.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series178.0ms

Calls
3 calls:
Slowest
91.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
67.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
19.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify3.9s

Calls
75 calls:
Slowest
432.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
374.0ms
(/ (* (* (/ rand (sqrt 9)) (/ rand (sqrt 9))) (/ rand (sqrt 9))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
258.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
215.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
155.0ms
(- (* 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))))))

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-exp-log add-cube-cbrt
7×pow1
6×associate-/r* add-cbrt-cube sqrt-div associate-*r* sqrt-prod
4×expm1-log1p-u associate-*l* associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- div-inv flip--
2×rec-exp pow1/2 prod-exp pow-flip
1×frac-times rem-sqrt-square clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative cbrt-unprod fma-udef inv-pow
Calls
4 calls:
Slowest
6.0ms
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
1.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series197.0ms

Calls
4 calls:
Slowest
68.0ms
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
59.0ms
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
44.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
26.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify2.8s

Calls
45 calls:
Slowest
378.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
352.0ms
(* (* (* (/ rand (sqrt 9)) (/ rand (sqrt 9))) (/ rand (sqrt 9))) (* (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (/ 1 (sqrt (- a (/ 1.0 3.0))))))
257.0ms
(- (sqrt -3.0) (+ (* 4.5 (/ a (sqrt -3.0))) (+ (* 13.5 (/ (pow a 2) (sqrt -3.0))) (* 10.125 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
232.0ms
(+ (log (/ rand (sqrt 9))) (log (/ 1 (sqrt (- a (/ 1.0 3.0))))))
219.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))

prune989.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.3s27369×body80nan
1.3s9161×body80valid