Details

Time bar (total: 1.3m)

sample525.0ms

Algorithm
intervals
Results
271.0ms93×body2560valid
130.0ms82×body1280valid
85.0ms53×body640valid
12.0ms256×pre80true
11.0ms16×body320valid
3.0ms8×body160valid
1.0ms4×body80valid

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: 59.5b

localize21.0ms

Local error

Found 2 expressions with local error:

3.0b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite86.0ms

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
65.0ms
(- (/ 1 x) (/ 1 (tan x)))
12.0ms
(/ 1 (tan x))

series121.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(- (/ 1 x) (/ 1 (tan x)))
39.0ms
(/ 1 (tan x))

simplify49.5s

Counts
440 → 268
Calls
440 calls:
Slowest
465.0ms
(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))))))
432.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) x) (- (* (/ (sqrt 1) (sqrt (tan x))) (/ (sqrt 1) (sqrt (tan x))))))
420.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
416.0ms
(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))))))
408.0ms
(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: 0.3b

localize17.0ms

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)

rewrite12.0ms

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
6.0ms
(* x (fma x (* 1/45 x) 1/3))
5.0ms
(* 1/45 x)
0.0ms
(fma x (* 1/45 x) 1/3)

series249.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
137.0ms
(* x (fma x (* 1/45 x) 1/3))
80.0ms
(fma x (* 1/45 x) 1/3)
31.0ms
(* 1/45 x)

simplify1.8s

Counts
30 → 64
Calls
30 calls:
Slowest
808.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
205.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
190.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
175.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
129.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune704.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1 add-cbrt-cube add-exp-log
14×add-sqr-sqrt
11×pow-prod-down prod-exp cbrt-unprod
10×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×unswap-sqr
Counts
4 → 87
Calls
4 calls:
Slowest
48.0ms
(* (* x (* 1/45 x)) x)
31.0ms
(* x (* 1/45 x))
11.0ms
(* 1/3 x)
11.0ms
(* 1/45 x)

series139.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(* (* x (* 1/45 x)) x)
34.0ms
(* x (* 1/45 x))
25.0ms
(* 1/45 x)
16.0ms
(* 1/3 x)

simplify3.1s

Counts
49 → 99
Calls
49 calls:
Slowest
656.0ms
(* (* (* (* x x) x) (* (* (* 1/45 x) (* 1/45 x)) (* 1/45 x))) (* (* x x) x))
522.0ms
(* (* (* (* x x) x) (* (* (* 1/45 1/45) 1/45) (* (* x x) x))) (* (* x x) x))
499.0ms
(* (* (* (* x (* 1/45 x)) (* x (* 1/45 x))) (* x (* 1/45 x))) (* (* x x) x))
245.0ms
(* (* (* x x) x) (* (* (* 1/45 x) (* 1/45 x)) (* 1/45 x)))
215.0ms
(* (* (* 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

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.5b
(* (cbrt x) (cbrt x))

rewrite16.0ms

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
Counts
4 → 85
Calls
4 calls:
Slowest
12.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(* (cbrt x) (cbrt x))
296.0ms
(cbrt x)
288.0ms
(cbrt x)
258.0ms
(cbrt x)

simplify881.0ms

Counts
63 → 97
Calls
63 calls:
Slowest
149.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
109.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
106.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
94.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
77.0ms
(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes99.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
10.2s3283×body2560valid
4.7s2484×body1280valid
1.2s1279×body640valid
342.0ms602×body320valid
336.0ms8000×pre80true
114.0ms301×body160valid
10.0ms51×body80valid