Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
9.0ms	44×	body	640	valid
7.0ms	137×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify62.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

62.0ms

(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

Slowest

84.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
28.0ms	(/ (+ x 1) (- x 1))
15.0ms	(/ x (+ x 1))

series162.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

97.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
37.0ms	(/ x (+ x 1))
29.0ms	(/ (+ x 1) (- x 1))

simplify5.2m

Counts

1382 → 762

Calls

1382 calls:

Slowest

821.0ms	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
800.0ms	(fma (/ 1 1) (/ x (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))
794.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
786.0ms	(fma (/ (sqrt x) 1) (/ (sqrt x) (+ x 1)) (- (* (/ (cbrt (+ x 1)) (cbrt (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))))))
778.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune4.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

27.9b	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 62

Calls

4 calls:

Slowest

3.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))
0.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
36.0ms	(cbrt (+ x 1))
36.0ms	(cbrt (+ x 1))
32.0ms	(cbrt (+ x 1))

simplify1.8s

Counts

30 → 74

Calls

30 calls:

Slowest

182.0ms	(- (+ (* (pow x 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1)))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (+ (* 2 (/ 1 x)) 1)))
165.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
160.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
160.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
143.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune563.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

27.9b	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
27.9b	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
27.9b	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.3b	(cbrt (* (* (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1)))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 46

Calls

4 calls:

Slowest

10.0ms	(cbrt (* (* (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1)))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))))
0.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
124.0ms	(cbrt (* (* (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1)))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))))
120.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
118.0ms	(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))

simplify1.5s

Counts

14 → 58

Calls

14 calls:

Slowest

471.0ms	(cbrt (* (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1)))) (fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))))
182.0ms	(- (+ (* (pow x 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1)))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (+ (* 2 (/ 1 x)) 1)))
182.0ms	(- (+ (* (pow x 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1)))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (+ (* 2 (/ 1 x)) 1)))
180.0ms	(- (+ (* (pow x 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1)))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (+ (* 2 (/ 1 x)) 1)))
179.0ms	(- (+ (* (pow x 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1)))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ -1 x)) (log -1))))) (+ (* 2 (/ 1 x)) 1)))

prune471.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

28.6b	(fma (/ x (fma x (* x x) 1)) (+ (* x x) (- (* 1 1) (* x 1))) (- (/ (+ x 1) (- x 1))))
4.8b	(/ x (fma x (* x x) 1))
0.1b	(fma x (* x x) 1)
0.0b	(/ (+ x 1) (- x 1))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
37×	`times-frac`
25×	`add-cube-cbrt`
10×	`associate-/r*` `difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/r/` `fma-udef` `div-inv` `associate-/l/`
1×	`flip3-+` `flip3--` `flip-+` `flip--`

Counts

4 → 110

Calls

4 calls:

Slowest

18.0ms	(/ (+ x 1) (- x 1))
8.0ms	(/ x (fma x (* x x) 1))
0.0ms	(fma (/ x (fma x (* x x) 1)) (+ (* x x) (- (* 1 1) (* x 1))) (- (/ (+ x 1) (- x 1))))
0.0ms	(fma x (* x x) 1)

series281.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

111.0ms	(fma (/ x (fma x (* x x) 1)) (+ (* x x) (- (* 1 1) (* x 1))) (- (/ (+ x 1) (- x 1))))
80.0ms	(/ x (fma x (* x x) 1))
68.0ms	(fma x (* x x) 1)
22.0ms	(/ (+ x 1) (- x 1))

simplify3.3s

Counts

108 → 122

Calls

108 calls:

Slowest

288.0ms	(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
223.0ms	(- (+ (/ 1 (pow x 8)) (/ 1 (pow x 2))) (/ 1 (pow x 5)))
216.0ms	(- (+ (/ 1 (pow x 8)) (/ 1 (pow x 2))) (/ 1 (pow x 5)))
178.0ms	(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))
174.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune777.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.2b

bsearch102.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

523.0ms	1700×	body	1280	valid
299.0ms	1316×	body	640	valid
265.0ms	4047×	body	80	valid
133.0ms	610×	body	320	valid
34.0ms	327×	body	160	valid