Details

Time bar (total: 46.5s)

sample791.0ms

Algorithm
intervals
Results
370.0ms59×body2560valid
254.0ms74×body1280valid
82.0ms64×body640valid
26.0ms33×body320valid
11.0ms15×body160valid
4.0ms11×body80valid

simplify71.0ms

Calls
1 calls:
Slowest
70.0ms
(/ (- x (sin x)) (- x (tan x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite10.0ms

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
5.0ms
(/ (- x (sin x)) (- x (tan x)))
2.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series672.0ms

Calls
3 calls:
Slowest
537.0ms
(/ (- x (sin x)) (- x (tan x)))
73.0ms
(- x (tan x))
61.0ms
(- x (sin x))

simplify2.3s

Calls
39 calls:
Slowest
409.0ms
(- (+ 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)))))
381.0ms
(- (+ 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)))))
307.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
269.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
146.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune666.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.5b
(expm1 (/ (- x (sin x)) (- x (tan x))))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
5×log1p-expm1-u
4×expm1-log1p-u pow1 flip3-- insert-posit16 flip-- add-log-exp
3×associate-/r* associate-/l*
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv expm1-log1p clear-num frac-2neg div-sub div-exp div-inv expm1-udef
Calls
4 calls:
Slowest
3.0ms
(/ (- x (sin x)) (- x (tan x)))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))
0.0ms
(expm1 (/ (- x (sin x)) (- x (tan x))))

series414.0ms

Calls
4 calls:
Slowest
151.0ms
(expm1 (/ (- x (sin x)) (- x (tan x))))
110.0ms
(- x (tan x))
104.0ms
(/ (- x (sin x)) (- x (tan x)))
49.0ms
(- x (sin x))

simplify3.9s

Calls
43 calls:
Slowest
597.0ms
(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
586.0ms
(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
448.0ms
(- (+ 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)))))
405.0ms
(- (+ 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)))))
315.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune824.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

23.3b
(log1p (fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1))
0.1b
(fma (* x x) 9/40 1)
0.1b
(fma 351/22400 (pow x 4) (fma (* x x) 9/40 1))
0.1b
(fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×log1p-udef log1p-expm1
Calls
4 calls:
Slowest
0.0ms
(log1p (fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1))
0.0ms
(fma (* x x) 9/40 1)
0.0ms
(fma 351/22400 (pow x 4) (fma (* x x) 9/40 1))
0.0ms
(fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1)

series705.0ms

Calls
4 calls:
Slowest
421.0ms
(log1p (fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1))
160.0ms
(fma (fma 351/22400 (pow x 4) (fma (* x x) 9/40 1)) (exp -1/2) -1)
64.0ms
(fma 351/22400 (pow x 4) (fma (* x x) 9/40 1))
60.0ms
(fma (* x x) 9/40 1)

simplify2.0s

Calls
13 calls:
Slowest
347.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
329.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
279.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
271.0ms
(- (+ (log (* 351/22400 (exp -1/2))) (* 560/39 (/ 1 (pow x 2)))) (+ (* 4 (log (/ 1 x))) (* 179200/4563 (/ 1 (pow x 4)))))
254.0ms
(- (+ (log (* 351/22400 (exp -1/2))) (* 560/39 (/ 1 (pow x 2)))) (+ (* 4 (log (/ -1 x))) (* 179200/4563 (/ 1 (pow x 4)))))

prune678.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (fma (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x) (- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))))
0.8b
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
0.1b
(/ (sin x) (cos x))
0.1b
(/ (sin x) (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
11×flip3-+ flip-+
10×frac-sub
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-*l/ associate-/l* add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u frac-times pow1 insert-posit16
3×fma-neg prod-diff
2×cbrt-undiv quot-tan clear-num frac-2neg div-exp associate-*r/ div-inv sub-div
1×expm1-log1p sub-neg flip3-- diff-log associate--l+ flip-- expm1-udef
Calls
4 calls:
Slowest
23.0ms
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
4.0ms
(/ (sin x) (cos x))
4.0ms
(/ (sin x) (cos x))
0.0ms
(expm1 (fma (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x) (- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))))

series427.0ms

Calls
4 calls:
Slowest
194.0ms
(expm1 (fma (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x) (- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))))
179.0ms
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
35.0ms
(/ (sin x) (cos x))
20.0ms
(/ (sin x) (cos x))

simplify13.5s

Calls
96 calls:
Slowest
869.0ms
(* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) (* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) x))
814.0ms
(* (- 1 (/ (/ (sin x) (cos x)) x)) (* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) x))
767.0ms
(* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) (* (- 1 (/ (/ (sin x) (cos x)) x)) x))
686.0ms
(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
615.0ms
(- (+ (pow 1 3) (pow (/ (/ (sin x) (cos x)) x) 3)) (* (+ (pow 1 3) (pow (/ (/ (sin x) (cos x)) x) 3)) (/ (sin x) x)))

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch176.0ms

end0.0ms

sample17.1s

Algorithm
intervals
Results
7.7s1706×body2560valid
5.8s2597×body1280valid
2.4s1982×body640valid
750.0ms943×body320valid
212.0ms435×body160valid
87.0ms337×body80valid