Details

Time bar (total: 1.5m)

sample470.0ms

Algorithm
intervals
Results
292.0ms92×body2560valid
96.0ms76×body1280valid
45.0ms52×body640valid
11.0ms19×body320valid
10.0ms256×pre80true
5.0ms16×body160valid
0.0ms1×body80valid

simplify30.0ms

Calls
1 calls:
Slowest
30.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize21.0ms

Local error

Found 2 expressions with local error:

3.9b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
268×add-sqr-sqrt
260×*-un-lft-identity
244×add-cube-cbrt
182×prod-diff
81×frac-sub
57×associate-/r* associate-/l*
33×div-inv
19×clear-num frac-2neg
14×tan-quot associate-/r/
13×fma-neg
9×difference-of-squares
7×distribute-lft-out--
6×add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
1×cbrt-undiv rec-exp sub-neg flip3-- diff-log 1-exp pow-flip flip-- inv-pow
Calls
2 calls:
Slowest
63.0ms
(- (/ 1 x) (/ 1 (tan x)))
12.0ms
(/ 1 (tan x))

series140.0ms

Calls
2 calls:
Slowest
97.0ms
(- (/ 1 x) (/ 1 (tan x)))
42.0ms
(/ 1 (tan x))

simplify59.5s

Calls
600 calls:
Slowest
690.0ms
(- (* (/ 1 (sqrt x)) (- (tan x))) (* (sqrt x) (- 1)))
606.0ms
(- (* (- 1) (cbrt (tan x))) (* (- x) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
539.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) x) (- (* (/ (sqrt 1) (sqrt (tan x))) (/ (sqrt 1) (sqrt (tan x))))))
511.0ms
(- (* (/ 1 (* (cbrt x) (cbrt x))) (cbrt (tan x))) (* (cbrt x) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
467.0ms
(- (* 1 (cbrt (tan x))) (* (/ x 1) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))

prune2.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (fma x (* 1/45 x) 1/3))
0.2b
(* 1/45 x)
0.0b
(fma x (* 1/45 x) 1/3)
0.0b
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in
Calls
4 calls:
Slowest
9.0ms
(* 1/45 x)
6.0ms
(* x (fma x (* 1/45 x) 1/3))
0.0ms
(fma x (* 1/45 x) 1/3)
0.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

series309.0ms

Calls
4 calls:
Slowest
120.0ms
(* x (fma x (* 1/45 x) 1/3))
94.0ms
(fma x (* 1/45 x) 1/3)
80.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
15.0ms
(* 1/45 x)

simplify2.7s

Calls
33 calls:
Slowest
727.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
358.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
324.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
323.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
189.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune842.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
0.2b
(* 1/45 x)
0.2b
(* 1/45 x)
0.0b
(fma x (* 1/45 x) 1/3)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
41×associate-*r*
26×sqrt-prod
21×unswap-sqr
18×*-un-lft-identity add-cube-cbrt
15×associate-*l*
13×pow1 add-cbrt-cube add-exp-log
12×swap-sqr
5×pow-prod-down prod-exp *-commutative cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×fma-udef
Calls
4 calls:
Slowest
48.0ms
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
10.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)
0.0ms
(fma x (* 1/45 x) 1/3)

series256.0ms

Calls
4 calls:
Slowest
144.0ms
(* x (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))))
71.0ms
(fma x (* 1/45 x) 1/3)
26.0ms
(* 1/45 x)
15.0ms
(* 1/45 x)

simplify3.0s

Calls
89 calls:
Slowest
199.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
183.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
179.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
150.0ms
(* (* (* x x) x) (* (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))))
131.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b
(* x (fma 1/45 (* x x) 1/3))
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×fma-udef
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
3 calls:
Slowest
11.0ms
(* x (fma 1/45 (* x x) 1/3))
0.0ms
(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))
0.0ms
(fma 1/45 (* x x) 1/3)

series354.0ms

Calls
3 calls:
Slowest
164.0ms
(* x (fma 1/45 (* x x) 1/3))
102.0ms
(fma 1/45 (* x x) 1/3)
87.0ms
(fma (pow x 5) 2/945 (* x (fma 1/45 (* x x) 1/3)))

simplify2.5s

Calls
21 calls:
Slowest
810.0ms
(* (* (* x x) x) (* (* (fma 1/45 (* x x) 1/3) (fma 1/45 (* x x) 1/3)) (fma 1/45 (* x x) 1/3)))
352.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
317.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
290.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
172.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune840.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes56.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample16.5s

Algorithm
intervals
Results
9.5s3180×body2560valid
4.2s2585×body1280valid
1.7s1237×body640valid
415.0ms623×body320valid
363.0ms8000×pre80true
126.0ms320×body160valid
10.0ms55×body80valid