Details

Time bar (total: 4.4m)

sample1.1s

Algorithm
intervals
Results
500.0ms55×body2560valid
262.0ms96×body1280valid
135.0ms56×body640valid
19.0ms22×body320valid
9.0ms15×body160valid
5.0ms12×body80valid

simplify111.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
110.0ms
(/ (- x (sin x)) (- x (tan x)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize38.0ms

Local error

Found 3 expressions with local error:

1.4b
(- x (tan x))
1.2b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite121.0ms

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
86.0ms
(/ (- x (sin x)) (- x (tan x)))
15.0ms
(- x (tan x))
12.0ms
(- x (sin x))

series578.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
210.0ms
(/ (- x (sin x)) (- x (tan x)))
193.0ms
(- x (tan x))
174.0ms
(- x (sin x))

simplify9.6s

Counts
173 → 122
Calls
173 calls:
Slowest
746.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
548.0ms
(- (+ 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)))))
462.0ms
(- (+ 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)))))
425.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
405.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))

prune987.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

series133.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
73.0ms
(fma (* x x) -27/2800 9/40)
60.0ms
(fma (* x x) (fma (* x x) -27/2800 9/40) -1/2)

simplify2.6s

Counts
28 → 28
Calls
28 calls:
Slowest
311.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
295.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
284.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
247.0ms
(* (* (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))
200.0ms
(exp (fma (* x x) (fma (* x x) -27/2800 9/40) -1/2))

prune273.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
0.8b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
678×times-frac
459×prod-diff
417×add-cube-cbrt
147×distribute-lft-out--
141×difference-of-squares
92×associate-/r/
49×flip3-- flip--
46×div-inv
27×fma-neg
10×add-log-exp
6×add-cbrt-cube add-exp-log
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×sub-neg distribute-rgt-out-- diff-log associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 592
Calls
4 calls:
Slowest
92.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
18.0ms
(/ (sin x) (- x (tan x)))
10.0ms
(- x (tan x))
10.0ms
(- x (tan x))

series514.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
73.0ms
(- x (tan x))
70.0ms
(- x (tan x))
70.0ms
(/ (sin x) (- x (tan x)))

simplify3.5m

Counts
1092 → 604
Calls
1092 calls:
Slowest
902.0ms
(fma (/ (sqrt x) 1) (/ (sqrt x) (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
767.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ (cbrt x) (cbrt (- x (tan x)))) (- (* (/ (cbrt (sin x)) (sqrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (- x (tan x)))))))
735.0ms
(fma (/ (sqrt x) (sqrt (- x (tan x)))) (/ (sqrt x) (sqrt (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
728.0ms
(fma (/ 1 (+ (sqrt x) (sqrt (tan x)))) (/ x (- (sqrt x) (sqrt (tan x)))) (- (* (cbrt (/ (sin x) (- x (tan x)))) (* (cbrt (/ (sin x) (- x (tan x)))) (cbrt (/ (sin x) (- x (tan x))))))))
645.0ms
(fma x (/ 1 (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))

prune5.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
36×prod-diff
32×add-cube-cbrt
12×fma-neg add-log-exp
4×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 116
Calls
4 calls:
Slowest
19.0ms
(- x (tan x))
11.0ms
(- x (tan x))
6.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series265.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(- x (tan x))
72.0ms
(- x (tan x))
63.0ms
(- x (tan x))
58.0ms
(- x (tan x))

simplify9.2s

Counts
176 → 128
Calls
176 calls:
Slowest
407.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
379.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
375.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
367.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))
342.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

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

bsearch106.0ms

end0.0ms

sample17.2s

Algorithm
intervals
Results
7.3s1619×body2560valid
6.5s2818×body1280valid
2.1s1814×body640valid
742.0ms912×body320valid
242.0ms498×body160valid
87.0ms339×body80valid