Details

Time bar (total: 1.1m)

sample769.0ms

Algorithm
intervals
Results
245.0ms100×body1280valid
244.0ms37×body2560valid
62.0ms60×body640valid
24.0ms31×body320valid
9.0ms18×body160valid
3.0ms10×body80valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(/ (- x (sin x)) (- x (tan x)))

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize38.0ms

Local error

Found 3 expressions with local error:

2.1b
(- x (tan x))
2.1b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 113
Calls
3 calls:
Slowest
37.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (tan x))
12.0ms
(- x (sin x))

series252.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(- x (tan x))
92.0ms
(/ (- x (sin x)) (- x (tan x)))
62.0ms
(- x (sin x))

simplify5.7s

Counts
122 → 122
Calls
122 calls:
Slowest
435.0ms
(- (+ 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)))))
434.0ms
(- (+ 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)))))
400.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
291.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
251.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune944.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

12.6b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b
(* (* x x) (* x x))
0.1b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
114×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
15×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
3×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
3 → 88
Calls
3 calls:
Slowest
41.0ms
(* (* x x) (* x x))
0.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series262.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
59.0ms
(* (* x x) (* x x))
51.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify2.7s

Counts
76 → 97
Calls
76 calls:
Slowest
391.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
353.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
341.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
264.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
160.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune831.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

30.2b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
2.1b
(- x (sin x))
1.3b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.6b
(cbrt x)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-cbrt-cube add-exp-log add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-prod associate-/r* fma-neg
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg pow1/3 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 95
Calls
4 calls:
Slowest
14.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
6.0ms
(- x (sin x))
1.0ms
(cbrt x)
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
741.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
479.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
256.0ms
(cbrt x)
45.0ms
(- x (sin x))

simplify3.9s

Counts
80 → 107
Calls
80 calls:
Slowest
449.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))))
216.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
202.0ms
(- (* 1/3 (pow x 3)))
143.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))
136.0ms
(fma (sqrt x) (sqrt x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune996.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.1b
(- x (tan x))
2.1b
(- x (sin x))
0.0b
(/ (- x (tan x)) (- x (sin x)))
0.0b
(/ 1 (/ (- x (tan x)) (- x (sin x))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
218×times-frac
214×add-sqr-sqrt *-un-lft-identity
106×add-cube-cbrt
54×distribute-lft-out-- difference-of-squares
36×associate-/r*
18×prod-diff
17×add-exp-log
11×add-cbrt-cube associate-/r/
8×flip3-- div-exp flip-- associate-/l* add-log-exp
6×fma-neg div-inv
5×pow1
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u
2×rec-exp clear-num sub-neg frac-2neg diff-log 1-exp associate-/l/
1×div-sub pow-flip inv-pow
Counts
4 → 264
Calls
4 calls:
Slowest
32.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
27.0ms
(/ (- x (tan x)) (- x (sin x)))
10.0ms
(- x (sin x))
5.0ms
(- x (tan x))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
123.0ms
(/ (- x (tan x)) (- x (sin x)))
97.0ms
(- x (tan x))
45.0ms
(- x (sin x))

simplify26.3s

Counts
352 → 276
Calls
352 calls:
Slowest
534.0ms
(- (+ 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)))))
530.0ms
(/ (cbrt 1) (/ (cbrt (- x (tan x))) (- (sqrt x) (sqrt (sin x)))))
476.0ms
(/ (* (* 1 1) 1) (* (* (/ (- x (tan x)) (- x (sin x))) (/ (- x (tan x)) (- x (sin x)))) (/ (- x (tan x)) (- x (sin x)))))
443.0ms
(- (+ 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
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))) (+ (sqrt x) (sqrt (sin x)))))

prune2.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes88.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch175.0ms

end0.0ms

sample16.5s

Algorithm
intervals
Results
6.5s1544×body2560valid
6.1s2768×body1280valid
2.8s1887×body640valid
670.0ms944×body320valid
221.0ms497×body160valid
89.0ms360×body80valid