Details

Time bar (total: 2.2m)

sample163.0ms

Algorithm
intervals
Results
99.0ms902×body80nan
31.0ms294×body80valid

simplify648.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
647.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×*-un-lft-identity
83×add-cube-cbrt
78×prod-diff
67×times-frac
41×distribute-rgt-in distribute-lft-in
9×pow1
8×add-cbrt-cube add-exp-log
7×div-inv
6×associate-*r* associate-*r/
5×sqrt-prod
4×expm1-log1p-u associate-/r* sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*l* flip-- associate-/l*
2×sub-neg sqrt-pow1 pow-prod-down associate-/r/ difference-of-squares
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp prod-exp *-commutative cbrt-unprod fma-udef distribute-lft-out-- unswap-sqr
Counts
4 → 171
Calls
4 calls:
Slowest
27.0ms
(* 9 (- a (/ 1.0 3.0)))
20.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
14.0ms
(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)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
100.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
93.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
54.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.4s

Counts
148 → 183
Calls
148 calls:
Slowest
585.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
460.0ms
(* 9 (fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))))))
431.0ms
(* (fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))))) 9)
407.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
401.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
13×times-frac
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-*l* associate-*l/
5×sqrt-prod
4×expm1-log1p-u associate-/r* sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*r* flip-- associate-/l*
2×sqrt-pow1 pow-prod-down associate-/r/ difference-of-squares
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp prod-exp *-commutative cbrt-unprod fma-udef div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 89
Calls
4 calls:
Slowest
48.0ms
(* (- a (/ 1.0 3.0)) 9)
17.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
12.0ms
(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9)))
0.0ms
(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9)))
137.0ms
(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
84.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
74.0ms
(* (- a (/ 1.0 3.0)) 9)

simplify5.6s

Counts
64 → 101
Calls
64 calls:
Slowest
407.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
348.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9)
343.0ms
(sqrt (* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9))
339.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (* (- a (/ 1.0 3.0)) 9)) (sqrt (* (- a (/ 1.0 3.0)) 9))) (sqrt (* (- a (/ 1.0 3.0)) 9))))
315.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) 9)

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))
0.3b
(* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)
0.2b
(/ rand (sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))))
0.1b
(sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×associate-*l/
24×*-un-lft-identity
17×pow1
16×sqrt-div associate-*l* add-cube-cbrt sqrt-prod
14×times-frac
13×add-cbrt-cube add-exp-log
12×frac-times
10×flip3-- flip--
9×flip3-+ flip-+
8×associate-/r/
7×pow-prod-down
6×associate-*r/ difference-of-squares
4×expm1-log1p-u associate-/r* associate-*r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 associate-/l*
2×*-commutative distribute-lft-out distribute-lft-out--
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp div-inv unswap-sqr
Counts
4 → 127
Calls
4 calls:
Slowest
468.0ms
(* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))
66.0ms
(/ rand (sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))))
44.0ms
(sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)))
30.0ms
(* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)

series4.9s

Counts
4 → 12
Calls
4 calls:
Slowest
3.3s
(/ rand (sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))))
1.2s
(sqrt (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)))
338.0ms
(* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9))
112.0ms
(* (- (sqrt a) (sqrt (/ 1.0 3.0))) 9)

simplify16.0s

Counts
103 → 139
Calls
103 calls:
Slowest
683.0ms
(sqrt (* (- (* (sqrt a) (sqrt a)) (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0)))) (* (- (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)) 9)))
667.0ms
(sqrt (* (+ (* (sqrt a) (sqrt a)) (- (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0))) (* (sqrt a) (sqrt (/ 1.0 3.0))))) (+ (* (sqrt a) (sqrt a)) (+ (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0))) (* (sqrt a) (sqrt (/ 1.0 3.0)))))))
632.0ms
(* (+ (* (sqrt a) (sqrt a)) (- (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0))) (* (sqrt a) (sqrt (/ 1.0 3.0))))) (+ (* (sqrt a) (sqrt a)) (+ (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0))) (* (sqrt a) (sqrt (/ 1.0 3.0))))))
629.0ms
(sqrt (* (+ (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)) (* (- (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)) 9)))
602.0ms
(* (+ (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)) (* (- (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)) 9))

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
282×sqrt-prod
188×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
44×sqrt-div
30×associate-/l*
24×associate-*l/
20×associate-/r/
14×associate-/r*
12×flip3-- flip--
11×add-cbrt-cube add-exp-log
10×pow1 div-inv
4×expm1-log1p-u cbrt-undiv sqrt-pow1 div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow1/2 pow-prod-down
1×associate-/l/
Counts
4 → 323
Calls
4 calls:
Slowest
48.0ms
(/ (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))
24.0ms
(/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))
10.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
9.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))

series777.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))
285.0ms
(/ (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))
99.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
62.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))

simplify1.1m

Counts
493 → 335
Calls
493 calls:
Slowest
741.0ms
(/ (* (* (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))) (/ rand (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))) (* (* (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))))
673.0ms
(/ (/ rand (sqrt (sqrt (* (- (pow a 3) (pow (/ 1.0 3.0) 3)) 9)))) (sqrt (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))))
454.0ms
(- (/ (* (sqrt -3.0) rand) (pow (sqrt 3) 2)) (+ (* 10.125 (/ (* (pow a 2) rand) (* (pow (sqrt -3.0) 3) (pow (sqrt 3) 2)))) (+ (* 4.5 (/ (* a rand) (* (sqrt -3.0) (pow (sqrt 3) 2)))) (* 13.5 (/ (* (pow a 2) rand) (* (sqrt -3.0) (pow (sqrt 3) 2)))))))
449.0ms
(/ (/ (* (* rand rand) rand) (* (* (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))) (* (* (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))))
445.0ms
(/ (/ rand (sqrt (sqrt (* (- (pow a 3) (pow (/ 1.0 3.0) 3)) 9)))) (* (cbrt (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9)))) (cbrt (sqrt (sqrt (* (- a (/ 1.0 3.0)) 9))))))

prune4.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.0s26867×body80nan
1.6s9092×body80valid