Details

Time bar (total: 2.4m)

sample201.0ms

Algorithm
intervals
Results
124.0ms859×body80nan
37.0ms290×body80valid

simplify282.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
282.0ms
(* (- 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

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 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)))

rewrite82.0ms

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
48.0ms
(* 9 (- a (/ 1.0 3.0)))
16.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
12.0ms
(/ 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)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
99.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
88.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
71.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify53.5s

Counts
280 → 183
Calls
280 calls:
Slowest
825.0ms
(* 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))))))
785.0ms
(* (* (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
773.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
580.0ms
(* (* (* 9 (- a (/ 1.0 3.0))) (* 9 (- a (/ 1.0 3.0)))) (* 9 (- a (/ 1.0 3.0))))
478.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ rand (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
64×times-frac
56×*-un-lft-identity
49×sqrt-prod
40×add-cube-cbrt
33×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×associate-/r*
8×distribute-lft-out--
7×pow1
6×sqrt-div
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*l* flip-- associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative fma-udef
Counts
4 → 144
Calls
4 calls:
Slowest
41.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
21.0ms
(sqrt (- a (/ 1.0 3.0)))
11.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
0.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
141.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
116.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
46.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify13.7s

Counts
192 → 156
Calls
192 calls:
Slowest
1.1s
(* (* (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
380.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
309.0ms
(* (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
304.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (/ rand (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt (- a (/ 1.0 3.0))))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
302.0ms
(* 1/3 (/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
106×times-frac
86×sqrt-prod
71×*-un-lft-identity
65×add-cube-cbrt
32×add-exp-log
27×associate-*r* associate-*l*
20×add-cbrt-cube sqrt-div
15×pow1 unswap-sqr
14×associate-/r*
12×sqrt-pow1
11×div-exp associate-*r/
8×prod-exp associate-/r/
6×cbrt-undiv pow-flip associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1/2 cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp pow-prod-down
2×clear-num frac-2neg
1×frac-times rem-sqrt-square associate-*l/ *-commutative inv-pow
Counts
4 → 223
Calls
4 calls:
Slowest
135.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))
38.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
14.0ms
(sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))
13.0ms
(/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))
321.0ms
(/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
222.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
198.0ms
(sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify40.7s

Counts
297 → 235
Calls
297 calls:
Slowest
530.0ms
(* (* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (* (* (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))))
517.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt 9))))
493.0ms
(* (* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))) (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))))
438.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ (* (cbrt rand) (cbrt rand)) (sqrt (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))))
436.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3)))))))

prune3.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
0.6b
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
0.6b
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
0.5b
(* (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(* (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))))
2.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
1.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
1.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
399.0ms
(* (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))))
329.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
309.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
297.0ms
(cbrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))

simplify18.5s

Counts
111 → 97
Calls
111 calls:
Slowest
622.0ms
(* (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
567.0ms
(* (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
560.0ms
(cbrt (sqrt (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))))
296.0ms
(- (+ (pow 0.1111111111111111 1/3) (* 2/9 (* (pow -0.3333333333333333 1/6) rand))) (* 2.0 (* a (pow 0.1111111111111111 1/3))))
289.0ms
(- (+ (* 1/9 (* rand (pow -3.0 1/6))) (pow (- 0.3333333333333333) 1/3)) (* 1.0 (* a (pow -0.3333333333333333 1/3))))

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes174.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
4.7s27167×body80nan
1.3s9124×body80valid