Details

Time bar (total: 1.4m)

sample433.0ms

Algorithm
intervals
Results
268.0ms100×body2560valid
101.0ms90×body1280valid
24.0ms35×body640valid
12.0ms21×body320valid
10.0ms256×pre80true
4.0ms9×body160valid
0.0ms1×body80valid

simplify77.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize21.0ms

Local error

Found 2 expressions with local error:

2.2b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite35.0ms

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
23.0ms
(- (/ 1 x) (/ 1 (tan x)))
6.0ms
(/ 1 (tan x))

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
87.0ms
(- (/ 1 x) (/ 1 (tan x)))
39.0ms
(/ 1 (tan x))

simplify49.8s

Counts
440 → 268
Calls
440 calls:
Slowest
451.0ms
(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))
439.0ms
(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)))))))
433.0ms
(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))))))
403.0ms
(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))))))
397.0ms
(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))))))

prune1.9s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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)))

rewrite12.0ms

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
6.0ms
(* x (fma x (* 1/45 x) 1/3))
5.0ms
(* 1/45 x)
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)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(* x (fma x (* 1/45 x) 1/3))
100.0ms
(fma x (* 1/45 x) 1/3)
92.0ms
(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
15.0ms
(* 1/45 x)

simplify2.8s

Counts
33 → 78
Calls
33 calls:
Slowest
751.0ms
(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
427.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
320.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
296.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
218.0ms
(* (* (* 1/45 1/45) 1/45) (* (* x x) x))

prune731.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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
34.0ms
(* (* 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)
8.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(* x (sqrt (fma x (* 1/45 x) 1/3)))
123.0ms
(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
26.0ms
(* 1/45 x)
26.0ms
(* 1/45 x)

simplify2.8s

Counts
57 → 103
Calls
57 calls:
Slowest
267.0ms
(* (* (* 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))))
214.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
210.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
202.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
188.0ms
(* (* (* (* 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))))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1 add-cbrt-cube add-exp-log
21×associate-*r*
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×sqrt-prod
11×pow-prod-down prod-exp cbrt-unprod
8×associate-*l*
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×unswap-sqr
Counts
4 → 96
Calls
4 calls:
Slowest
116.0ms
(* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (fma x (* 1/45 x) 1/3)))
26.0ms
(* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))
5.0ms
(* 1/45 x)
5.0ms
(* 1/45 x)

series389.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))
146.0ms
(* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (fma x (* 1/45 x) 1/3)))
29.0ms
(* 1/45 x)
27.0ms
(* 1/45 x)

simplify3.8s

Counts
61 → 108
Calls
61 calls:
Slowest
324.0ms
(* (* (* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (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))))
295.0ms
(* (* (* (* x x) x) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))))
279.0ms
(* (* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* (sqrt (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))))
225.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
221.0ms
(* (* (* (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (sqrt (fma x (* 1/45 x) 1/3))))) (* (* x (sqrt (sqrt (fma x (* 1/45 x) 1/3)))) (sqrt (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))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample15.8s

Algorithm
intervals
Results
8.9s3304×body2560valid
4.3s2475×body1280valid
1.3s1319×body640valid
679.0ms8000×pre80true
376.0ms595×body320valid
93.0ms258×body160valid
9.0ms49×body80valid