Details

Time bar (total: 1.3m)

sample499.0ms

Algorithm
intervals
Results
260.0ms93×body2560valid
152.0ms88×body1280valid
44.0ms47×body640valid
12.0ms256×pre80true
11.0ms13×body320valid
6.0ms15×body160valid

simplify61.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
61.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize25.0ms

Local error

Found 2 expressions with local error:

3.7b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite31.0ms

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
17.0ms
(- (/ 1 x) (/ 1 (tan x)))
6.0ms
(/ 1 (tan x))

series513.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
473.0ms
(- (/ 1 x) (/ 1 (tan x)))
40.0ms
(/ 1 (tan x))

simplify48.2s

Counts
440 → 268
Calls
440 calls:
Slowest
416.0ms
(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)))))))
407.0ms
(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
407.0ms
(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))))))
407.0ms
(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))))))
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))))))

prune1.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 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)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
3×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
Counts
3 → 55
Calls
3 calls:
Slowest
5.0ms
(* x (fma x (* 1/45 x) 1/3))
5.0ms
(* 1/45 x)
0.0ms
(fma x (* 1/45 x) 1/3)

series253.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(* x (fma x (* 1/45 x) 1/3))
84.0ms
(fma x (* 1/45 x) 1/3)
27.0ms
(* 1/45 x)

simplify1.9s

Counts
30 → 64
Calls
30 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)))
190.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
163.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
153.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
138.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune672.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x 1/3)
0.2b
(* 1/45 x)
0.1b
(* x (* 1/45 x))
0.1b
(* x (* x (* 1/45 x)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1 add-cbrt-cube add-exp-log
14×add-sqr-sqrt
12×associate-*l*
11×pow-prod-down prod-exp cbrt-unprod
10×*-un-lft-identity add-cube-cbrt
8×associate-*r*
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×unswap-sqr
Counts
4 → 87
Calls
4 calls:
Slowest
66.0ms
(* x (* x (* 1/45 x)))
25.0ms
(* x (* 1/45 x))
10.0ms
(* x 1/3)
10.0ms
(* 1/45 x)

series99.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
40.0ms
(* x (* x (* 1/45 x)))
27.0ms
(* x (* 1/45 x))
16.0ms
(* x 1/3)
15.0ms
(* 1/45 x)

simplify3.1s

Counts
50 → 99
Calls
50 calls:
Slowest
615.0ms
(* (* (* x x) x) (* (* (* x (* 1/45 x)) (* x (* 1/45 x))) (* x (* 1/45 x))))
610.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* (* 1/45 x) (* 1/45 x)) (* 1/45 x))))
469.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* (* 1/45 1/45) 1/45) (* (* x x) x))))
267.0ms
(* (* (* x x) x) (* (* (* 1/45 x) (* 1/45 x)) (* 1/45 x)))
213.0ms
(* (* (* x x) x) (* (* (* 1/45 1/45) 1/45) (* (* x x) x)))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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
25.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
14.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
5.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(* 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)
27.0ms
(* 1/45 x)

simplify2.8s

Counts
57 → 103
Calls
57 calls:
Slowest
267.0ms
(* (* (* 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
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
196.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
194.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
176.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes72.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample16.4s

Algorithm
intervals
Results
10.2s3189×body2560valid
3.8s2504×body1280valid
1.2s1288×body640valid
423.0ms664×body320valid
343.0ms8000×pre80true
120.0ms316×body160valid
7.0ms39×body80valid