Details

sample62.0ms

Algorithm

intervals

Results

19.0ms	45×	body	640	valid
18.0ms	51×	body	1280	valid
10.0ms	137×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

(- (cbrt (+ x 1)) (cbrt x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize22.0ms

Local error

Found 3 expressions with local error:

2.3b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 102

Calls

3 calls:

Slowest

59.0ms	(- (cbrt (+ x 1)) (cbrt x))
3.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)

series457.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

289.0ms	(cbrt x)
122.0ms	(- (cbrt (+ x 1)) (cbrt x))
45.0ms	(cbrt (+ x 1))

simplify7.0s

Counts

122 → 111

Calls

122 calls:

Slowest

350.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
296.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
283.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
226.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
191.0ms	(- (+ (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))))

prune923.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.6b

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (cbrt (+ x 1)) (cbrt x))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))
0.0b	(expm1 (log1p (- (cbrt (+ x 1)) (cbrt x))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
57×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
34×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`expm1-log1p` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `expm1-udef`

Counts

4 → 114

Calls

4 calls:

Slowest

48.0ms	(- (cbrt (+ x 1)) (cbrt x))
3.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)
0.0ms	(expm1 (log1p (- (cbrt (+ x 1)) (cbrt x))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

303.0ms	(cbrt x)
175.0ms	(expm1 (log1p (- (cbrt (+ x 1)) (cbrt x))))
93.0ms	(- (cbrt (+ x 1)) (cbrt x))
55.0ms	(cbrt (+ x 1))

simplify8.1s

Counts

126 → 126

Calls

126 calls:

Slowest

388.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
322.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
312.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))
291.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2)))))
274.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (* 5/81 (pow (/ 1 (pow x 8)) 1/3))) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.6b

localize48.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

Slowest

38.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series953.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

296.0ms	(cbrt x)
288.0ms	(cbrt x)
246.0ms	(cbrt x)
123.0ms	(- (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt x) (cbrt x)))

simplify1.6s

Counts

27 → 72

Calls

27 calls:

Slowest

296.0ms	(- (+ (* 4/81 (pow (/ 1 (pow x 7)) 1/3)) (* 2/3 (pow (/ 1 x) 1/3))) (* 1/9 (pow (/ 1 (pow x 4)) 1/3)))
265.0ms	(- (+ (* 2/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 2/3)))
209.0ms	(/ (exp (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (exp (* (cbrt x) (cbrt x))))
179.0ms	(- (+ (* 2/3 (pow (/ 1 x) 1/3)) (pow (/ -1 x) -2/3)) (+ (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2)) (* 1/9 (pow (/ 1 (pow x 4)) 1/3))))
139.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune920.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

28.3b	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
0.6b	(cbrt x)
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

3.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(cbrt x)
142.0ms	(fma (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))) (- (cbrt x)))
49.0ms	(cbrt (+ x 1))
41.0ms	(cbrt (+ x 1))

simplify3.1s

Counts

27 → 71

Calls

27 calls:

Slowest

597.0ms	(- (+ (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))))
395.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow x 1/3)) (+ (pow (/ 1 x) -1/3) (* 1/9 (pow (/ 1 (pow x 5)) 1/3))))
361.0ms	(- (+ (* 1/3 (* (pow (/ 1 (pow x 7)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (* (pow (pow x 2) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x))))))) (+ (* (pow (* x -1) 1/3) (cbrt -1)) (* 1/9 (* (pow (/ 1 (pow x 16)) 1/9) (exp (* 1/9 (- (log -1) (log (/ -1 x)))))))))
262.0ms	(- (+ (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))))
252.0ms	(- (+ (* 1/3 x) 1) (+ (* 1/9 (pow x 2)) (pow x 1/3)))

prune772.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

regimes88.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 30.3b

bsearch190.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

586.0ms	1716×	body	1280	valid
338.0ms	4038×	body	80	valid
283.0ms	1311×	body	640	valid
98.0ms	611×	body	320	valid
72.0ms	324×	body	160	valid