Details

Time bar (total: 30.8s)

sample513.0ms

Algorithm
intervals
Results
145.0ms48×body2560valid
144.0ms96×body1280valid
74.0ms53×body640valid
43.0ms15×body80valid
14.0ms28×body320valid
5.0ms16×body160valid

simplify156.0ms

Calls
1 calls:
Slowest
155.0ms
(/ (- x (sin x)) (- x (tan x)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize19.0ms

Local error

Found 3 expressions with local error:

2.2b
(- x (tan x))
2.2b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
4.0ms
(/ (- x (sin x)) (- x (tan x)))
2.0ms
(- x (tan x))
1.0ms
(- x (sin x))

series268.0ms

Calls
3 calls:
Slowest
118.0ms
(/ (- x (sin x)) (- x (tan x)))
105.0ms
(- x (tan x))
45.0ms
(- x (sin x))

simplify2.4s

Calls
39 calls:
Slowest
429.0ms
(- (+ 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)))))
391.0ms
(- (+ 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)))))
332.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
299.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
184.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune633.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

14.4b
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.2b
(* 9/40 x)
0.1b
(fma (* 9/40 x) x -1/2)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
1.0ms
(* 9/40 x)
0.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.0ms
(fma (* 9/40 x) x -1/2)

series60.0ms

Calls
3 calls:
Slowest
29.0ms
(fma (* 9/40 x) x -1/2)
24.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
7.0ms
(* 9/40 x)

simplify429.0ms

Calls
9 calls:
Slowest
122.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
117.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
100.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
34.0ms
(- (* 9/40 (pow x 2)) 1/2)
19.0ms
(- (* 9/40 (pow x 2)) 1/2)

prune425.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

14.4b
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (cbrt (fma (* 9/40 x) x -1/2))))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
0.0ms
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (cbrt (fma (* 9/40 x) x -1/2))))

series403.0ms

Calls
4 calls:
Slowest
140.0ms
(cbrt (fma (* 9/40 x) x -1/2))
130.0ms
(cbrt (fma (* 9/40 x) x -1/2))
111.0ms
(cbrt (fma (* 9/40 x) x -1/2))
21.0ms
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (cbrt (fma (* 9/40 x) x -1/2))))

simplify2.8s

Calls
21 calls:
Slowest
341.0ms
(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/400 (* (pow x 4) (pow -1/2 1/3)))))
329.0ms
(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/400 (* (pow x 4) (pow -1/2 1/3)))))
302.0ms
(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/400 (* (pow x 4) (pow -1/2 1/3)))))
271.0ms
(- (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (+ (* 400/729 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (pow x 4))) (* 20/27 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (pow x 2)))))
245.0ms
(- (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (+ (* 400/729 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (pow x 4))) (* 20/27 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x)))))) (pow x 2)))))

prune491.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

16.8b
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (log1p (expm1 (cbrt (fma (* 9/40 x) x -1/2))))))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))
13.8b
(cbrt (fma (* 9/40 x) x -1/2))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
1.0ms
(cbrt (fma (* 9/40 x) x -1/2))
0.0ms
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (log1p (expm1 (cbrt (fma (* 9/40 x) x -1/2))))))

series684.0ms

Calls
4 calls:
Slowest
301.0ms
(fma (pow x 4) -27/2800 (* (* (cbrt (fma (* 9/40 x) x -1/2)) (cbrt (fma (* 9/40 x) x -1/2))) (log1p (expm1 (cbrt (fma (* 9/40 x) x -1/2))))))
152.0ms
(cbrt (fma (* 9/40 x) x -1/2))
124.0ms
(cbrt (fma (* 9/40 x) x -1/2))
106.0ms
(cbrt (fma (* 9/40 x) x -1/2))

simplify3.9s

Calls
21 calls:
Slowest
551.0ms
(- (* (exp (* 1/3 (- (log 81/1600) (* 4 (log (/ -1 x)))))) (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x))))))) (+ (* 20/9 (/ (* (exp (* 1/3 (- (log 81/1600) (* 4 (log (/ -1 x)))))) (exp (* 1/3 (- (log 9/40) (* 2 (log (/ -1 x))))))) (pow x 2))) (* 27/2800 (pow x 4))))
529.0ms
(- (exp (* 1/3 (- (log 9/40) (* 2 (log (/ 1 x)))))) (+ (* 400/729 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ 1 x)))))) (pow x 4))) (* 20/27 (/ (exp (* 1/3 (- (log 9/40) (* 2 (log (/ 1 x)))))) (pow x 2)))))
404.0ms
(- (* (exp (* 1/3 (- (log 9/40) (* 2 (log (/ 1 x)))))) (exp (* 1/3 (- (log 81/1600) (* 4 (log (/ 1 x))))))) (+ (* 27/2800 (pow x 4)) (* 20/9 (/ (* (exp (* 1/3 (- (log 9/40) (* 2 (log (/ 1 x)))))) (exp (* 1/3 (- (log 81/1600) (* 4 (log (/ 1 x))))))) (pow x 2)))))
368.0ms
(- (pow -1/8 1/3) (+ (* 9/20 (* (pow x 2) (pow -1/8 1/3))) (* 27/2800 (pow x 4))))
308.0ms
(- (pow -1/2 1/3) (+ (* 3/20 (* (pow x 2) (pow -1/2 1/3))) (* 9/400 (* (pow x 4) (pow -1/2 1/3)))))

prune640.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch121.0ms

end0.0ms

sample16.7s

Algorithm
intervals
Results
7.6s1605×body2560valid
5.9s2753×body1280valid
2.1s1818×body640valid
705.0ms1000×body320valid
252.0ms432×body160valid
99.0ms392×body80valid