Details

Time bar (total: 4.2m)

sample556.0ms

Algorithm
intervals
Results
202.0ms48×body2560valid
119.0ms87×body1280valid
114.0ms64×body640valid
23.0ms31×body320valid
6.0ms12×body160valid
3.0ms14×body80valid

simplify35.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
35.0ms
(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize63.0ms

Local error

Found 3 expressions with local error:

1.4b
(- x (sin x))
1.4b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite67.0ms

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
39.0ms
(/ (- x (sin x)) (- x (tan x)))
14.0ms
(- x (sin x))
9.0ms
(- x (tan x))

series196.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
86.0ms
(/ (- x (sin x)) (- x (tan x)))
56.0ms
(- x (tan x))
54.0ms
(- x (sin x))

simplify5.8s

Counts
122 → 122
Calls
122 calls:
Slowest
532.0ms
(- (+ 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)))))
433.0ms
(- (+ 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)))))
331.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
324.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
236.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.3b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite130.0ms

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
81.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
18.0ms
(/ (sin x) (- x (tan x)))
8.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
264.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
98.0ms
(- x (tan x))
87.0ms
(- x (tan x))
82.0ms
(/ (sin x) (- x (tan x)))

simplify3.4m

Counts
1036 → 604
Calls
1036 calls:
Slowest
848.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
836.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
757.0ms
(fma (/ 1 1) (/ x (- x (tan x))) (- (* (/ (cbrt (sin x)) (cbrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
641.0ms
(fma x (/ 1 (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
620.0ms
(fma (- (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x))))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x)))) (* (/ (sqrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (sqrt (sin x)) (+ (sqrt x) (sqrt (tan x))))))

prune5.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (sin x))
1.4b
(- x (sin x))
1.4b
(- x (sin x))
1.4b
(- x (tan x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
36×prod-diff
32×add-cube-cbrt
12×fma-neg add-log-exp
4×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 116
Calls
4 calls:
Slowest
12.0ms
(- x (sin x))
12.0ms
(- x (sin x))
12.0ms
(- x (sin x))
10.0ms
(- x (tan x))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(- x (tan x))
67.0ms
(- x (sin x))
54.0ms
(- x (sin x))
40.0ms
(- x (sin x))

simplify5.9s

Counts
108 → 128
Calls
108 calls:
Slowest
279.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
229.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
201.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
175.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
174.0ms
(fma 1 x (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma (/ (/ x (+ x (tan x))) (- x (tan x))) (+ x (tan x)) (- (/ (sin x) (- x (tan x)))))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
0.1b
(/ (sin x) (- x (tan x)))

rewrite36.0ms

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
23.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))
0.0ms
(fma (/ (/ x (+ x (tan x))) (- x (tan x))) (+ x (tan x)) (- (/ (sin x) (- x (tan x)))))

series898.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
638.0ms
(fma (/ (/ x (+ x (tan x))) (- x (tan x))) (+ x (tan x)) (- (/ (sin x) (- x (tan x)))))
106.0ms
(/ (sin x) (- x (tan x)))
84.0ms
(- x (tan x))
69.0ms
(- x (tan x))

simplify5.5s

Counts
101 → 121
Calls
101 calls:
Slowest
518.0ms
(- (+ 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)))))
494.0ms
(- (+ 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)))))
269.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
265.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
207.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch206.0ms

end0.0ms

sample17.2s

Algorithm
intervals
Results
7.2s1551×body2560valid
5.6s2810×body1280valid
3.0s1866×body640valid
761.0ms928×body320valid
275.0ms462×body160valid
98.0ms383×body80valid