Details

Time bar (total: 31.5s)

sample456.0ms

Algorithm
intervals
Results
275.0ms112×body2560valid
120.0ms80×body1280valid
28.0ms38×body640valid
10.0ms256×pre80true
7.0ms15×body320valid
4.0ms11×body160valid

simplify32.0ms

Calls
1 calls:
Slowest
32.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize25.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×prod-diff
17×*-un-lft-identity
15×add-sqr-sqrt div-inv
13×add-cube-cbrt
5×tan-quot associate-/r/
4×fma-neg distribute-lft-out-- add-log-exp
3×pow1 associate-/r* add-exp-log
2×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
1×rec-exp clear-num sub-neg frac-2neg flip3-- diff-log frac-sub pow-flip flip-- inv-pow difference-of-squares
Calls
2 calls:
Slowest
11.0ms
(- (/ 1 x) (/ 1 (tan x)))
2.0ms
(/ 1 (tan x))

series124.0ms

Calls
2 calls:
Slowest
96.0ms
(- (/ 1 x) (/ 1 (tan x)))
27.0ms
(/ 1 (tan x))

simplify3.1s

Calls
62 calls:
Slowest
298.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
120.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
113.0ms
(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))
105.0ms
(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))
101.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))

prune431.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (fma 1/45 (* x x) 1/3) x)
0.0b
(fma 1/45 (* x x) 1/3)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×*-commutative fma-udef
Calls
2 calls:
Slowest
3.0ms
(* (fma 1/45 (* x x) 1/3) x)
0.0ms
(fma 1/45 (* x x) 1/3)

series168.0ms

Calls
2 calls:
Slowest
104.0ms
(* (fma 1/45 (* x x) 1/3) x)
63.0ms
(fma 1/45 (* x x) 1/3)

simplify267.0ms

Calls
8 calls:
Slowest
57.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
56.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
45.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
28.0ms
(+ (* 1/45 (pow x 2)) 1/3)
24.0ms
(+ (* 1/45 (pow x 2)) 1/3)

prune237.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
0.0b
(sqrt (fma 1/45 (* x x) 1/3))
0.0b
(sqrt (fma 1/45 (* x x) 1/3))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l* sqrt-prod
10×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 *-commutative
1×associate-*r* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
5.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
1.0ms
(sqrt (fma 1/45 (* x x) 1/3))
1.0ms
(sqrt (fma 1/45 (* x x) 1/3))

series409.0ms

Calls
4 calls:
Slowest
135.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
100.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
89.0ms
(sqrt (fma 1/45 (* x x) 1/3))
85.0ms
(sqrt (fma 1/45 (* x x) 1/3))

simplify3.4s

Calls
33 calls:
Slowest
516.0ms
(* (* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))) (* (* (* (sqrt (fma 1/45 (* x x) 1/3)) x) (* (sqrt (fma 1/45 (* x x) 1/3)) x)) (* (sqrt (fma 1/45 (* x x) 1/3)) x)))
371.0ms
(- (+ (sqrt 1/3) (* 1/90 (/ (pow x 2) (sqrt 1/3)))) (* 1/16200 (/ (pow x 4) (pow (sqrt 1/3) 3))))
358.0ms
(- (+ (sqrt 1/3) (* 1/90 (/ (pow x 2) (sqrt 1/3)))) (* 1/16200 (/ (pow x 4) (pow (sqrt 1/3) 3))))
314.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
250.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))

prune762.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
0.3b
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
0.1b
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
0.0b
(sqrt (fma 1/45 (* x x) 1/3))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*l* sqrt-prod
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×associate-*r*
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
46.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
13.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
4.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
1.0ms
(sqrt (fma 1/45 (* x x) 1/3))

series1.0s

Calls
4 calls:
Slowest
661.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
187.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
133.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
67.0ms
(sqrt (fma 1/45 (* x x) 1/3))

simplify4.6s

Calls
47 calls:
Slowest
456.0ms
(- (+ (sqrt 1/3) (* 1/90 (/ (pow x 2) (sqrt 1/3)))) (* 1/16200 (/ (pow x 4) (pow (sqrt 1/3) 3))))
348.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
332.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
320.0ms
(- (+ (* x (pow 1/3 1/4)) (* 1/60 (* (pow x 3) (pow 1/3 1/4)))) (* 1/2400 (* (pow x 5) (pow 1/3 1/4))))
319.0ms
(- (+ (* x (exp (* 1/4 (- (log 1/45) (* 2 (log (/ -1 x))))))) (* 15/4 (/ (exp (* 1/4 (- (log 1/45) (* 2 (log (/ -1 x)))))) x))) (* 675/32 (/ (exp (* 1/4 (- (log 1/45) (* 2 (log (/ -1 x)))))) (pow x 3))))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample15.1s

Algorithm
intervals
Results
8.7s3229×body2560valid
3.9s2590×body1280valid
1.0s1177×body640valid
817.0ms681×body320valid
344.0ms8000×pre80true
133.0ms280×body160valid
7.0ms43×body80valid