Details

Time bar (total: 1.3m)

sample477.0ms

Algorithm
intervals
Results
283.0ms98×body2560valid
116.0ms91×body1280valid
33.0ms40×body640valid
17.0ms256×pre80true
13.0ms23×body320valid
1.0ms4×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite51.0ms

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
Counts
2 → 262
Calls
2 calls:
Slowest
39.0ms
(- (/ 1 x) (/ 1 (tan x)))
6.0ms
(/ 1 (tan x))

series137.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
88.0ms
(- (/ 1 x) (/ 1 (tan x)))
48.0ms
(/ 1 (tan x))

simplify48.1s

Counts
440 → 268
Calls
440 calls:
Slowest
656.0ms
(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))))))
405.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
397.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt x) (cbrt x))) (/ (cbrt 1) (cbrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
390.0ms
(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))))))
389.0ms
(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))))))

prune1.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.4b
(* x (fma x (* 1/45 x) 1/3))
0.2b
(* 1/45 x)

rewrite14.0ms

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
Counts
2 → 44
Calls
2 calls:
Slowest
7.0ms
(* 1/45 x)
6.0ms
(* x (fma x (* 1/45 x) 1/3))

series148.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
133.0ms
(* x (fma x (* 1/45 x) 1/3))
15.0ms
(* 1/45 x)

simplify1.6s

Counts
27 → 50
Calls
27 calls:
Slowest
745.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
211.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
137.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
126.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
121.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune513.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

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)))
0.2b
(* 1/45 x)
0.2b
(* 1/45 x)

rewrite63.0ms

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
Counts
4 → 91
Calls
4 calls:
Slowest
32.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
15.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
9.0ms
(* 1/45 x)
6.0ms
(* 1/45 x)

series444.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
162.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
29.0ms
(* 1/45 x)
27.0ms
(* 1/45 x)

simplify2.8s

Counts
57 → 103
Calls
57 calls:
Slowest
277.0ms
(* (* (* 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))))
232.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
206.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
205.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
167.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

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
(* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))
0.2b
(* 1/45 x)
0.2b
(* 1/45 x)

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1 add-cbrt-cube add-exp-log
21×associate-*r*
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×sqrt-prod
11×pow-prod-down prod-exp cbrt-unprod
8×associate-*l*
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×unswap-sqr
Counts
4 → 96
Calls
4 calls:
Slowest
93.0ms
(* (* (* 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)))
25.0ms
(* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))
6.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))
113.0ms
(* (* (* 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)
27.0ms
(* 1/45 x)

simplify3.9s

Counts
61 → 108
Calls
61 calls:
Slowest
301.0ms
(* (* (* (* 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)))))
285.0ms
(* (* (* (* (* 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))))
249.0ms
(* (* (* (* 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)))))
217.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
213.0ms
(* (* (* (* (* 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))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample17.2s

Algorithm
intervals
Results
9.7s3216×body2560valid
4.6s2511×body1280valid
1.7s1261×body640valid
377.0ms628×body320valid
348.0ms8000×pre80true
162.0ms334×body160valid
10.0ms50×body80valid