Details

sample144.0ms

Algorithm

intervals

Results

122.0ms

639×

body

valid

simplify202.0ms

Calls

1 calls:

Slowest

202.0ms

(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1)

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(fma (* a a) a (* a a))
0.0b	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0b	(fma -3 a 1)

rewrite1.0ms

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` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (* a a) a (* a a))
0.0ms	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms	(fma -3 a 1)

series395.0ms

Calls

4 calls:

Slowest

141.0ms	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
109.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
104.0ms	(fma (* a a) a (* a a))
41.0ms	(fma -3 a 1)

simplify1.5s

Calls

12 calls:

Slowest

381.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
282.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
256.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
251.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
122.0ms	(- (+ (* 4 (pow a 2)) (* 4 (pow b 2))) 1)

prune978.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

2.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series745.0ms

Calls

4 calls:

Slowest

222.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
219.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
209.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
94.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

simplify2.4s

Calls

21 calls:

Slowest

302.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
301.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
301.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
279.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
276.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

2.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series901.0ms

Calls

4 calls:

Slowest

287.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
266.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
258.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
90.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

simplify4.9s

Calls

21 calls:

Slowest

532.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
494.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
432.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
284.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
269.0ms	(cbrt (* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.3b	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

1.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series1.1s

Calls

4 calls:

Slowest

334.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
281.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
262.0ms	(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
198.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

simplify5.0s

Calls

24 calls:

Slowest

593.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
535.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
509.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
289.0ms	(+ (* 4/3 (pow (/ 1 (pow b 2)) 1/3)) (pow (/ -1 b) -4/3))
285.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes273.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

5.5s

20611×

body

valid