Details

Time bar (total: 42.4s)

sample436.0ms

Algorithm
intervals
Results
194.0ms54×body2560valid
123.0ms80×body1280valid
46.0ms69×body640valid
14.0ms29×body320valid
4.0ms13×body160valid
2.0ms11×body80valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize57.0ms

Local error

Found 3 expressions with local error:

1.2b
(- x (tan x))
1.2b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite67.0ms

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))

series233.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
94.0ms
(/ (- x (sin x)) (- x (tan x)))
88.0ms
(- x (tan x))
51.0ms
(- x (sin x))

simplify9.1s

Counts
173 → 122
Calls
173 calls:
Slowest
527.0ms
(- (+ 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)))))
464.0ms
(- (+ 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)))))
410.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
360.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
344.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))

prune933.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

27.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
1.5b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.2b
(- x (sin x))
0.6b
(cbrt x)

rewrite50.0ms

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
29.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
11.0ms
(- x (sin x))
7.0ms
(cbrt x)
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
953.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
807.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
302.0ms
(cbrt x)
42.0ms
(- x (sin x))

simplify7.3s

Counts
138 → 107
Calls
138 calls:
Slowest
411.0ms
(* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))
404.0ms
(/ (* (* (- 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)))))
351.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
343.0ms
(* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (+ x (sin x)))
303.0ms
(- (* 1/3 (pow x 3)))

prune981.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (* x x) -27/2800 9/40)
0.0b
(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
2 → 22
Calls
2 calls:
Slowest
1.0ms
(fma (* x x) -27/2800 9/40)
0.0ms
(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

series181.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
105.0ms
(fma (* x x) -27/2800 9/40)
76.0ms
(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

simplify2.9s

Counts
28 → 28
Calls
28 calls:
Slowest
354.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
309.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
283.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
242.0ms
(* (* (fma (* x x) (fma (* x x) -27/2800 9/40) -1/2) (fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)) (fma (* x x) (fma (* x x) -27/2800 9/40) -1/2))
167.0ms
(exp (fma (* x x) (fma (* x x) -27/2800 9/40) -1/2))

prune201.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes71.0ms

Accuracy

100% (0.0b remaining)

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

bsearch235.0ms

end0.0ms

sample17.4s

Algorithm
intervals
Results
7.2s1674×body2560valid
5.9s2715×body1280valid
3.0s1832×body640valid
791.0ms963×body320valid
234.0ms480×body160valid
87.0ms336×body80valid