Details

sample139.0ms

Algorithm

intervals

Results

115.0ms

617×

body

valid

simplify170.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

169.0ms

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

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 (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

rewrite3.0ms

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`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(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))
145.0ms	(fma (* a a) a (* a a))
100.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
62.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.4s

Counts

12 → 56

Calls

12 calls:

Slowest

398.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
362.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
318.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
312.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
275.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune841.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

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 (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

rewrite2.0ms

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`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series466.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(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))
110.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
109.0ms	(fma (* a a) a (* a a))
70.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.4s

Counts

12 → 56

Calls

12 calls:

Slowest

435.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
385.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
380.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
314.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
289.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune944.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

Slowest

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

series477.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

210.0ms	(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)
92.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
81.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

simplify2.3s

Counts

15 → 59

Calls

15 calls:

Slowest

370.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
287.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
283.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
277.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
273.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
6×	`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`
2×	`pow1/3` `fma-udef`

Counts

4 → 51

Calls

4 calls:

Slowest

4.0ms	(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))))
1.0ms	(cbrt (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)
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series621.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

235.0ms	(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))))
185.0ms	(cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
123.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
78.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

simplify2.9s

Counts

19 → 63

Calls

19 calls:

Slowest

567.0ms	(cbrt (sqrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
342.0ms	(cbrt (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)))))
293.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
286.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
277.0ms	(cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

0% (0.5b remaining)

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

bsearch7.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

4.7s

20417×

body

valid