Details

Time bar (total: 1.3m)

sample523.0ms

Algorithm
intervals
Results
256.0ms91×body2560valid
149.0ms96×body1280valid
43.0ms8×body160valid
32.0ms34×body640valid
17.0ms27×body320valid
12.0ms256×pre80true

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
17.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize11.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite64.0ms

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
46.0ms
(- (/ 1 x) (/ 1 (tan x)))
7.0ms
(/ 1 (tan x))

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
87.0ms
(- (/ 1 x) (/ 1 (tan x)))
39.0ms
(/ 1 (tan x))

simplify48.6s

Counts
440 → 268
Calls
440 calls:
Slowest
597.0ms
(fma (/ 1 1) (/ 1 x) (- (* (/ (sqrt 1) (cbrt (tan x))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x)))))))
444.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
437.0ms
(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))))))
418.0ms
(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
(fma (/ (sqrt 1) (* (cbrt x) (cbrt x))) (/ (sqrt 1) (cbrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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
11.0ms
(* x (fma x (* 1/45 x) 1/3))
10.0ms
(* 1/45 x)

series162.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
141.0ms
(* x (fma x (* 1/45 x) 1/3))
21.0ms
(* 1/45 x)

simplify1.7s

Counts
27 → 50
Calls
27 calls:
Slowest
837.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
203.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
157.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
129.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
124.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune557.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

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)

rewrite60.0ms

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
35.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
9.0ms
(* 1/45 x)
8.0ms
(* 1/45 x)
7.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
140.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
28.0ms
(* 1/45 x)
25.0ms
(* 1/45 x)

simplify2.7s

Counts
57 → 103
Calls
57 calls:
Slowest
280.0ms
(* (* (* 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))))
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)))))
205.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
194.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
165.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×associate-*r*
13×*-un-lft-identity add-cube-cbrt
12×pow1 add-cbrt-cube associate-*l* add-exp-log
5×unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp *-commutative sqrt-prod cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 88
Calls
4 calls:
Slowest
11.0ms
(* 1/45 x)
11.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)
10.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
27.0ms
(* 1/45 x)
17.0ms
(* 1/45 x)
16.0ms
(* 1/45 x)

simplify2.0s

Counts
54 → 100
Calls
54 calls:
Slowest
338.0ms
(* (* (* 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))))
223.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
207.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
192.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
183.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes67.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample16.4s

Algorithm
intervals
Results
9.6s3277×body2560valid
3.7s2465×body1280valid
1.5s1258×body640valid
794.0ms642×body320valid
432.0ms8000×pre80true
115.0ms314×body160valid
9.0ms44×body80valid