Details

Time bar (total: 4.2m)

sample857.0ms

Algorithm
intervals
Results
303.0ms57×body2560valid
256.0ms93×body1280valid
124.0ms56×body640valid
59.0ms34×body320valid
5.0ms9×body160valid
2.0ms7×body80valid

simplify71.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
71.0ms
(/ (- x (sin x)) (- x (tan x)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.6b
(- x (tan x))
0.6b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 113
Calls
3 calls:
Slowest
41.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (tan x))
12.0ms
(- x (sin x))

series263.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
102.0ms
(/ (- x (sin x)) (- x (tan x)))
96.0ms
(- x (tan x))
66.0ms
(- x (sin x))

simplify5.9s

Counts
122 → 122
Calls
122 calls:
Slowest
513.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
507.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
359.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
241.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
238.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune920.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

16.8b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b
(* (* x x) (* x x))
0.0b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
114×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
15×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
3×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
3 → 88
Calls
3 calls:
Slowest
50.0ms
(* (* x x) (* x x))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

series249.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
134.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
75.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
39.0ms
(* (* x x) (* x x))

simplify2.6s

Counts
76 → 97
Calls
76 calls:
Slowest
348.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
320.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
295.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
294.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
169.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune789.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.6b
(- x (tan x))
0.6b
(- x (tan x))
0.1b
(/ (sin x) (- x (tan x)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
678×times-frac
459×prod-diff
417×add-cube-cbrt
147×distribute-lft-out--
141×difference-of-squares
92×associate-/r/
49×flip3-- flip--
46×div-inv
27×fma-neg
10×add-log-exp
6×add-cbrt-cube add-exp-log
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×sub-neg distribute-rgt-out-- diff-log associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 592
Calls
4 calls:
Slowest
85.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
13.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
73.0ms
(- x (tan x))
66.0ms
(/ (sin x) (- x (tan x)))
55.0ms
(- x (tan x))

simplify3.5m

Counts
1036 → 604
Calls
1036 calls:
Slowest
713.0ms
(fma (/ x (- (pow x 3) (pow (tan x) 3))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))) (- (* (/ (sin x) (- x (tan x))) (/ 1 1))))
713.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (- x (tan x))) (- (* (/ (sqrt (sin x)) (cbrt (- x (tan x)))) (/ (sqrt (sin x)) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
677.0ms
(fma (/ 1 1) (/ x (- x (tan x))) (- (* (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x)))))))
636.0ms
(fma (/ 1 (sqrt (- x (tan x)))) (/ x (sqrt (- x (tan x)))) (- (* (/ (cbrt (sin x)) (sqrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (- x (tan x)))))))
615.0ms
(fma (* (cbrt (/ x (- x (tan x)))) (cbrt (/ x (- x (tan x))))) (cbrt (/ x (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))

prune5.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
0.6b
(- x (tan x))
0.6b
(- x (tan x))
0.1b
(/ (sin x) (- x (tan x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
28×add-cube-cbrt
18×prod-diff
15×times-frac
8×add-log-exp
6×add-cbrt-cube fma-neg add-exp-log distribute-lft-out-- difference-of-squares
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×flip3-- flip-- associate-/l*
2×sub-neg diff-log associate-/r/
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 109
Calls
4 calls:
Slowest
21.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))
0.0ms
(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(fma x (/ 1 (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
84.0ms
(/ (sin x) (- x (tan x)))
74.0ms
(- x (tan x))
72.0ms
(- x (tan x))

simplify5.9s

Counts
101 → 121
Calls
101 calls:
Slowest
505.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
451.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
313.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
288.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
251.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch166.0ms

end0.0ms

sample17.5s

Algorithm
intervals
Results
7.1s1677×body2560valid
5.6s2724×body1280valid
3.5s1845×body640valid
799.0ms932×body320valid
216.0ms450×body160valid
100.0ms372×body80valid