Details

Time bar (total: 1.7m)

sample492.0ms

Algorithm
intervals
Results
304.0ms103×body2560valid
105.0ms76×body1280valid
36.0ms43×body640valid
16.0ms25×body320valid
12.0ms256×pre80true
4.0ms8×body160valid
0.0ms1×body80valid

simplify17.0ms

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

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.3b

localize25.0ms

Local error

Found 1 expressions with local error:

2.6b
(- (/ 1 x) (/ 1 (tan x)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
223×add-sqr-sqrt
215×*-un-lft-identity
199×add-cube-cbrt
182×prod-diff
32×div-inv
13×fma-neg tan-quot associate-/r/
9×difference-of-squares
7×distribute-lft-out--
3×add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log frac-sub insert-posit16 log1p-expm1-u flip--
Counts
1 → 227
Calls
1 calls:
Slowest
37.0ms
(- (/ 1 x) (/ 1 (tan x)))

series99.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
99.0ms
(- (/ 1 x) (/ 1 (tan x)))

simplify49.1s

Counts
409 → 230
Calls
409 calls:
Slowest
468.0ms
(fma (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt x)) (- (* (/ 1 (sqrt (tan x))) (/ 1 (sqrt (tan x))))))
451.0ms
(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))))))
448.0ms
(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))))))
439.0ms
(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))))))
430.0ms
(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)))))))

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.4b
(* x (fma x (* 1/45 x) 1/3))
0.2b
(* 1/45 x)
0.0b
(fma (pow x 5) 2/945 (* x (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 (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

series258.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
121.0ms
(* x (fma x (* 1/45 x) 1/3))
119.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
18.0ms
(* 1/45 x)

simplify2.7s

Counts
30 → 64
Calls
30 calls:
Slowest
782.0ms
(* (* (* 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))))
317.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
284.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
196.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune698.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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
16.0ms
(* (cbrt x) (cbrt x))
2.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
318.0ms
(cbrt x)
316.0ms
(* (cbrt x) (cbrt x))
294.0ms
(cbrt x)
264.0ms
(cbrt x)

simplify951.0ms

Counts
63 → 97
Calls
63 calls:
Slowest
134.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
130.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
127.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
117.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
83.0ms
(* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt x)) (cbrt (cbrt x))))

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize67.0ms

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)))))

rewrite22.0ms

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
16.0ms
(* (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))))

series962.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
240.0ms
(* (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)))))
235.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))
227.0ms
(cbrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))

simplify22.4s

Counts
65 → 97
Calls
65 calls:
Slowest
828.0ms
(* (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)))))))
542.0ms
(* (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
538.0ms
(* (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))
520.0ms
(* (sqrt (cbrt (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))))))
516.0ms
(* (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))) (cbrt (sqrt (fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3))))))

prune985.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.1b

regimes112.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample16.7s

Algorithm
intervals
Results
9.2s3195×body2560valid
5.0s2537×body1280valid
1.3s1270×body640valid
444.0ms8000×pre80true
399.0ms633×body320valid
117.0ms306×body160valid
11.0ms59×body80valid