Details

Time bar (total: 1.7m)

sample408.0ms

Algorithm
intervals
Results
258.0ms107×body2560valid
87.0ms88×body1280valid
21.0ms35×body640valid
17.0ms12×body320valid
9.0ms256×pre80true
4.0ms12×body160valid
0.0ms2×body80valid

simplify33.0ms

Calls
1 calls:
Slowest
32.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize20.0ms

Local error

Found 2 expressions with local error:

3.3b
(- (/ 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
Calls
2 calls:
Slowest
21.0ms
(- (/ 1 x) (/ 1 (tan x)))
18.0ms
(/ 1 (tan x))

series134.0ms

Calls
2 calls:
Slowest
76.0ms
(- (/ 1 x) (/ 1 (tan x)))
59.0ms
(/ 1 (tan x))

simplify48.5s

Calls
440 calls:
Slowest
709.0ms
(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))))))
457.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
401.0ms
(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))))))
397.0ms
(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))))))
385.0ms
(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)))))))

prune1.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (fma x (* 1/45 x) 1/3))
0.2b
(* 1/45 x)
0.0b
(fma x (* 1/45 x) 1/3)
0.0b
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in
Calls
4 calls:
Slowest
6.0ms
(* x (fma x (* 1/45 x) 1/3))
5.0ms
(* 1/45 x)
0.0ms
(fma x (* 1/45 x) 1/3)
0.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

series347.0ms

Calls
4 calls:
Slowest
143.0ms
(* x (fma x (* 1/45 x) 1/3))
91.0ms
(fma x (* 1/45 x) 1/3)
87.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
27.0ms
(* 1/45 x)

simplify2.7s

Calls
33 calls:
Slowest
850.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
334.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
306.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
264.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
204.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune733.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (log (exp (fma x (* 1/45 x) 1/3))))
0.2b
(* 1/45 x)
0.0b
(log (exp (fma x (* 1/45 x) 1/3)))
0.0b
(fma x (* 1/45 x) 1/3)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×log-prod
10×pow1 associate-*r*
8×add-cbrt-cube add-exp-log log-pow
6×exp-prod associate-*l*
4×distribute-rgt-in expm1-log1p-u distribute-lft-in fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-log-exp
Calls
4 calls:
Slowest
9.0ms
(* x (log (exp (fma x (* 1/45 x) 1/3))))
5.0ms
(* 1/45 x)
2.0ms
(log (exp (fma x (* 1/45 x) 1/3)))
0.0ms
(fma x (* 1/45 x) 1/3)

series364.0ms

Calls
4 calls:
Slowest
134.0ms
(* x (log (exp (fma x (* 1/45 x) 1/3))))
102.0ms
(fma x (* 1/45 x) 1/3)
100.0ms
(log (exp (fma x (* 1/45 x) 1/3)))
27.0ms
(* 1/45 x)

simplify4.4s

Calls
50 calls:
Slowest
871.0ms
(* (* (* x x) x) (* (* (log (exp (fma x (* 1/45 x) 1/3))) (log (exp (fma x (* 1/45 x) 1/3)))) (log (exp (fma x (* 1/45 x) 1/3)))))
265.0ms
(log (exp (* x (* 1/45 x))))
216.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
201.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
183.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.6b
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
0.5b
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))

rewrite21.0ms

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
Calls
4 calls:
Slowest
15.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
2.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
1.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
1.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))

series917.0ms

Calls
4 calls:
Slowest
269.0ms
(* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))
239.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
220.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
189.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))

simplify22.1s

Calls
65 calls:
Slowest
755.0ms
(* (cbrt (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
514.0ms
(* (cbrt (* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))) (cbrt (* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))))))
510.0ms
(cbrt (* (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))) (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
500.0ms
(+ (log (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (log (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
498.0ms
(* (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (sqrt (cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes102.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.1s3271×body2560valid
4.5s2524×body1280valid
1.1s1212×body640valid
489.0ms651×body320valid
332.0ms8000×pre80true
144.0ms296×body160valid
8.0ms46×body80valid