Details

Time bar (total: 3.1m)

sample144.0ms

Algorithm
intervals
Results
90.0ms848×body80nan
27.0ms291×body80valid

simplify309.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
308.0ms
(* (- 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: 0.0b

localize27.0ms

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
(- a (/ 1.0 3.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
50×*-un-lft-identity
48×add-cube-cbrt
40×times-frac
39×prod-diff
7×pow1
6×add-cbrt-cube add-exp-log add-log-exp
5×sqrt-prod
4×expm1-log1p-u associate-/r* sqrt-div associate-*r/ insert-posit16 log1p-expm1-u div-inv
3×flip3-- fma-neg flip-- associate-/l*
2×sqrt-pow1 associate-/r/ difference-of-squares
1×cbrt-undiv clear-num sub-neg frac-2neg pow1/2 diff-log div-exp pow-prod-down fma-udef distribute-lft-out--
Counts
4 → 123
Calls
4 calls:
Slowest
33.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
14.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
12.0ms
(- 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)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
113.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
101.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
25.0ms
(- a (/ 1.0 3.0))

simplify18.5s

Counts
137 → 135
Calls
137 calls:
Slowest
943.0ms
(fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
534.0ms
(fma (sqrt a) (sqrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
513.0ms
(fma 1 a (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
512.0ms
(fma (- (/ 1.0 (cbrt 3.0))) (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))))
481.0ms
(fma (- (/ 1.0 (cbrt 3.0))) (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×times-frac
23×*-un-lft-identity
22×add-cube-cbrt
18×associate-*r*
17×add-exp-log
13×pow1
11×add-cbrt-cube
8×sqrt-prod
7×associate-*r/
6×sqrt-div
4×expm1-log1p-u associate-/r* sqrt-pow1 div-exp prod-exp associate-/r/ insert-posit16 log1p-expm1-u pow-flip add-log-exp
3×flip3-- associate-*l* pow-prod-down flip-- associate-/l* unswap-sqr
2×cbrt-undiv rec-exp pow1/2 1-exp cbrt-unprod div-inv
1×clear-num frac-2neg un-div-inv *-commutative fma-udef inv-pow
Counts
4 → 114
Calls
4 calls:
Slowest
65.0ms
(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
17.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.0ms
(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
95.0ms
(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
85.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
82.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify8.6s

Counts
91 → 126
Calls
91 calls:
Slowest
686.0ms
(* (* (* rand rand) rand) (* (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))
449.0ms
(- (* 1/3 (sqrt -3.0)) (+ (* 1.5 (/ a (sqrt -3.0))) (+ (* 4.5 (/ (pow a 2) (sqrt -3.0))) (* 3.375 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
382.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
305.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
283.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt (* 9 (- a (/ 1.0 3.0))))))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 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
(- a (/ 1.0 3.0))
0.0b
(- a (/ 1.0 3.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
457×times-frac
375×add-sqr-sqrt
300×*-un-lft-identity
250×add-cube-cbrt
228×sqrt-prod
78×prod-diff
50×difference-of-squares
25×distribute-lft-out--
22×associate-/l*
17×div-inv
9×associate-/r* add-cbrt-cube add-exp-log
8×add-log-exp
6×fma-neg
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log associate-/r/
1×clear-num frac-2neg fma-udef associate-/l/
Counts
4 → 380
Calls
4 calls:
Slowest
21.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
7.0ms
(- a (/ 1.0 3.0))
7.0ms
(- 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)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
116.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
43.0ms
(- a (/ 1.0 3.0))
31.0ms
(- a (/ 1.0 3.0))

simplify53.3s

Counts
615 → 392
Calls
615 calls:
Slowest
583.0ms
(fma 1 a (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
574.0ms
(fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
556.0ms
(fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
538.0ms
(fma (- (/ 1.0 (cbrt 3.0))) (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))))
524.0ms
(fma 1 a (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))

prune4.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ rand (sqrt (cbrt 9)))
0.3b
(/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))
0.2b
(* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0)))))
0.1b
(fma (* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
1230×times-frac
941×add-sqr-sqrt
768×sqrt-prod
656×*-un-lft-identity
521×add-cube-cbrt
285×associate-*r*
189×cbrt-prod
126×difference-of-squares
63×distribute-lft-out--
50×add-exp-log
34×associate-/l*
32×add-cbrt-cube
27×unswap-sqr
23×div-inv
22×div-exp
18×associate-/r*
13×cbrt-undiv associate-*l*
12×prod-exp
6×pow1 cbrt-unprod
4×expm1-log1p-u sqrt-div associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg flip3-- flip--
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef associate-/l/
Counts
4 → 762
Calls
4 calls:
Slowest
70.0ms
(* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0)))))
17.0ms
(/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))
7.0ms
(/ rand (sqrt (cbrt 9)))
0.0ms
(fma (* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
675.0ms
(* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0)))))
405.0ms
(/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))
403.0ms
(fma (* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
198.0ms
(/ rand (sqrt (cbrt 9)))

simplify1.2m

Counts
1054 → 774
Calls
1054 calls:
Slowest
759.0ms
(- (/ (* rand (sqrt (/ -3.0 (cbrt 9)))) (fabs (cbrt 9))) (+ (* 4.5 (/ (* a rand) (* (fabs (cbrt 9)) (* (sqrt (/ -3.0 (cbrt 9))) (cbrt 9))))) (+ (* 10.125 (/ (* (pow a 2) rand) (* (fabs (cbrt 9)) (* (pow (cbrt 9) 2) (pow (sqrt (/ -3.0 (cbrt 9))) 3))))) (* 13.5 (/ (* (pow a 2) rand) (* (fabs (cbrt 9)) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9))))))))))
566.0ms
(/ (/ (* (cbrt rand) (cbrt rand)) (* (cbrt (sqrt (cbrt 9))) (cbrt (sqrt (cbrt 9))))) (sqrt (+ (sqrt a) (/ (sqrt 1.0) (sqrt 3.0)))))
524.0ms
(- (* rand (sqrt (/ -3.0 (cbrt 9)))) (+ (* 13.5 (/ (* (pow a 2) rand) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9)))))) (+ (* 10.125 (/ (* (pow a 2) rand) (* (pow (sqrt (/ -3.0 (cbrt 9))) 3) (pow (cbrt 9) 2)))) (* 4.5 (/ (* a rand) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9)))))))))
514.0ms
(+ (log (/ 1 (fabs (cbrt 9)))) (log (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0))))))
506.0ms
(* (/ 1 (fabs (cbrt 9))) (/ (/ rand (sqrt (cbrt 9))) (sqrt (- a (/ 1.0 3.0)))))

prune12.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes132.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.6s26878×body80nan
1.3s9100×body80valid