Details

sample151.0ms

Algorithm

intervals

Results

124.0ms

617×

body

valid

simplify232.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

232.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(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))
1.0ms	(fma (* a a) a (* a a))
1.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(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))
146.0ms	(fma (* a a) a (* a a))
113.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
101.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.8s

Counts

12 → 56

Calls

12 calls:

Slowest

485.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
400.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
394.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
347.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
327.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune946.0ms

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

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

series502.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(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))
120.0ms	(fma (* a a) a (* a a))
115.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
89.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.6s

Counts

12 → 56

Calls

12 calls:

Slowest

411.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
409.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
339.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
326.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
321.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune834.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

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))

rewrite4.0ms

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

2.0ms	(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)
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)

series590.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

225.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
132.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
118.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
116.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

simplify2.8s

Counts

15 → 59

Calls

15 calls:

Slowest

674.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
339.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
326.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
279.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
275.0ms	(+ (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

localize81.0ms

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)

rewrite12.0ms

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

8.0ms	(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))))
2.0ms	(cbrt (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)

series822.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

303.0ms	(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))))
290.0ms	(cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
118.0ms	(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)

simplify2.8s

Counts

19 → 63

Calls

19 calls:

Slowest

326.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
309.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
304.0ms	(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)))))
302.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
301.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.5b remaining)

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

bsearch4.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

5.1s

20417×

body

valid