Details

Time bar (total: 1.4m)

sample442.0ms

Algorithm
intervals
Results
279.0ms101×body2560valid
98.0ms83×body1280valid
26.0ms38×body640valid
10.0ms256×pre80true
9.0ms19×body320valid
5.0ms13×body160valid
0.0ms2×body80valid

simplify30.0ms

Counts
1 → 1
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: 59.8b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
208×add-cube-cbrt
182×prod-diff
33×div-inv
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 associate-/r* associate-/l*
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
2 → 262
Calls
2 calls:
Slowest
41.0ms
(- (/ 1 x) (/ 1 (tan x)))
12.0ms
(/ 1 (tan x))

series112.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
85.0ms
(- (/ 1 x) (/ 1 (tan x)))
27.0ms
(/ 1 (tan x))

simplify50.2s

Counts
440 → 268
Calls
440 calls:
Slowest
804.0ms
(fma (/ (sqrt 1) (* (cbrt x) (cbrt x))) (/ (sqrt 1) (cbrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
440.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
419.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt x) (cbrt x))) (/ (cbrt 1) (cbrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
400.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) x) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
394.0ms
(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (fma x (* 1/45 x) 1/3))
0.3b
(* 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)))

rewrite15.0ms

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
Counts
4 → 66
Calls
4 calls:
Slowest
7.0ms
(* 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)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* x (fma x (* 1/45 x) 1/3))
88.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
81.0ms
(fma x (* 1/45 x) 1/3)
21.0ms
(* 1/45 x)

simplify2.8s

Counts
33 → 78
Calls
33 calls:
Slowest
786.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
349.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
306.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
291.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
210.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune738.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×associate-*r*
15×pow1 add-cbrt-cube add-exp-log
13×*-un-lft-identity add-cube-cbrt
10×associate-*l*
7×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 91
Calls
4 calls:
Slowest
19.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
11.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
5.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
128.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
24.0ms
(* 1/45 x)
22.0ms
(* 1/45 x)

simplify2.6s

Counts
57 → 103
Calls
57 calls:
Slowest
300.0ms
(* (* (* 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))))
257.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
217.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
195.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
172.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×associate-*r*
13×*-un-lft-identity add-cube-cbrt
12×pow1 add-cbrt-cube associate-*l* add-exp-log
5×unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp *-commutative sqrt-prod cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 88
Calls
4 calls:
Slowest
14.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
11.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)
10.0ms
(* 1/45 x)

series206.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
26.0ms
(* 1/45 x)
19.0ms
(* 1/45 x)
15.0ms
(* 1/45 x)

simplify2.1s

Counts
54 → 100
Calls
54 calls:
Slowest
263.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
262.0ms
(* (* (* 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))))
238.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
215.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
205.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes76.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample17.0s

Algorithm
intervals
Results
10.1s3245×body2560valid
4.5s2495×body1280valid
1.3s1282×body640valid
442.0ms8000×pre80true
386.0ms618×body320valid
117.0ms317×body160valid
8.0ms43×body80valid