Details

Time bar (total: 1.3m)

sample453.0ms

Algorithm
intervals
Results
314.0ms117×body2560valid
72.0ms63×body1280valid
30.0ms44×body640valid
10.0ms256×pre80true
9.0ms19×body320valid
4.0ms12×body160valid
0.0ms1×body80valid

simplify67.0ms

Calls
1 calls:
Slowest
67.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize10.0ms

Local error

Found 2 expressions with local error:

2.9b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
208×add-cube-cbrt
182×prod-diff
33×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×difference-of-squares
7×distribute-lft-out--
6×add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Calls
2 calls:
Slowest
18.0ms
(- (/ 1 x) (/ 1 (tan x)))
6.0ms
(/ 1 (tan x))

series164.0ms

Calls
2 calls:
Slowest
112.0ms
(- (/ 1 x) (/ 1 (tan x)))
52.0ms
(/ 1 (tan x))

simplify49.9s

Calls
440 calls:
Slowest
655.0ms
(fma (- (/ (sqrt 1) (cbrt (tan x)))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (sqrt 1) (cbrt (tan x))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x))))))
443.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
398.0ms
(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
391.0ms
(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))
391.0ms
(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

0.3b
(* x (fma x (* 1/45 x) 1/3))
0.3b
(* 1/45 x)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
2×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
1×distribute-rgt-in distribute-lft-in
Calls
2 calls:
Slowest
12.0ms
(* x (fma x (* 1/45 x) 1/3))
10.0ms
(* 1/45 x)

series141.0ms

Calls
2 calls:
Slowest
118.0ms
(* x (fma x (* 1/45 x) 1/3))
23.0ms
(* 1/45 x)

simplify1.6s

Calls
27 calls:
Slowest
777.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
180.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
154.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
152.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
128.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune481.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(* x (sqrt (fma x (* 1/45 x) 1/3)))
0.4b
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
0.3b
(* 1/45 x)
0.3b
(* 1/45 x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×associate-*r*
15×pow1 add-cbrt-cube add-exp-log
13×*-un-lft-identity add-cube-cbrt
10×associate-*l*
7×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Calls
4 calls:
Slowest
20.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
7.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
5.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series360.0ms

Calls
4 calls:
Slowest
176.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
138.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
27.0ms
(* 1/45 x)
18.0ms
(* 1/45 x)

simplify2.9s

Calls
57 calls:
Slowest
325.0ms
(* (* (* x x) x) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
221.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
216.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
210.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
182.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (fma x (* 1/45 x) 1/3)))
0.3b
(* 1/45 x)
0.3b
(* 1/45 x)
0.3b
(* 1/45 x)

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-cbrt-cube add-exp-log
18×add-sqr-sqrt
15×associate-*r*
12×*-un-lft-identity add-cube-cbrt
10×associate-*l*
9×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod unswap-sqr
Calls
4 calls:
Slowest
101.0ms
(* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (fma x (* 1/45 x) 1/3)))
10.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)

series225.0ms

Calls
4 calls:
Slowest
151.0ms
(* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (fma x (* 1/45 x) 1/3)))
30.0ms
(* 1/45 x)
28.0ms
(* 1/45 x)
16.0ms
(* 1/45 x)

simplify2.5s

Calls
55 calls:
Slowest
283.0ms
(* (* (* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
224.0ms
(* (* (* (* (* x x) x) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
211.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
177.0ms
(* (* (* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
165.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample17.0s

Algorithm
intervals
Results
10.3s3339×body2560valid
4.2s2487×body1280valid
1.5s1202×body640valid
463.0ms633×body320valid
340.0ms8000×pre80true
117.0ms310×body160valid
6.0ms29×body80valid