Details

sample94.0ms

Algorithm

intervals

Results

79.0ms

621×

body

valid

simplify189.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

189.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
0.0b	(fma a a (* b b))
0.0b	(fma a a (* b b))
0.0b	(fma (* b b) 4 -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`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
89.0ms	(fma (* b b) 4 -1)
62.0ms	(fma a a (* b b))
49.0ms	(fma a a (* b b))

simplify917.0ms

Counts

12 → 56

Calls

12 calls:

Slowest

285.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
274.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
154.0ms	(- (+ (pow a 4) (* 4 (pow b 2))) 1)
36.0ms	(- (* 4 (pow b 2)) 1)
26.0ms	(+ (pow a 2) (pow b 2))

prune602.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

8.8b	(cbrt (fma a a (* b b)))
8.8b	(cbrt (fma a a (* b b)))
8.8b	(cbrt (fma a a (* b b)))
0.5b	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b))))
2.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(cbrt (fma a a (* b b)))
153.0ms	(* (cbrt (fma a a (* b b))) (cbrt (fma a a (* b b))))
135.0ms	(cbrt (fma a a (* b b)))
130.0ms	(cbrt (fma a a (* b b)))

simplify2.0s

Counts

65 → 97

Calls

65 calls:

Slowest

181.0ms	(+ (pow b 2/3) (* 1/3 (* (pow a 2) (pow (/ 1 (pow b 4)) 1/3))))
179.0ms	(+ (pow b 2/3) (* 1/3 (* (pow a 2) (pow (/ 1 (pow b 4)) 1/3))))
174.0ms	(+ (* 2/3 (* (pow a 2) (pow (/ 1 (pow b 2)) 1/3))) (pow b 4/3))
141.0ms	(+ (pow b 2/3) (* 1/3 (* (pow a 2) (pow (/ 1 (pow b 4)) 1/3))))
129.0ms	(* (* (cbrt (cbrt (fma a a (* b b)))) (cbrt (cbrt (fma a a (* b b))))) (* (cbrt (cbrt (fma a a (* b b)))) (cbrt (cbrt (fma a a (* b b))))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
8.8b	(cbrt (fma a a (* b b)))
0.3b	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
0.3b	(* (fma a a (* b b)) (fma a a (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`cbrt-prod` `pow1`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log`
7×	`associate-l`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down`
2×	`prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow3` `pow-sqr` `pow-prod-up`

Counts

4 → 86

Calls

4 calls:

Slowest

20.0ms	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
9.0ms	(* (fma a a (* b b)) (fma a a (* b b)))
5.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
1.0ms	(cbrt (fma a a (* b b)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(cbrt (fma a a (* b b)))
125.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
69.0ms	(* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (cbrt (fma a a (* b b))))
59.0ms	(* (fma a a (* b b)) (fma a a (* b b)))

simplify5.8s

Counts

61 → 98

Calls

61 calls:

Slowest

803.0ms	(* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b)))
742.0ms	(* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b)))
532.0ms	(* (* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b))) (* (* (fma a a (* b b)) (fma a a (* b b))) (fma a a (* b b))))
328.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
299.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
8.8b	(cbrt (fma a a (* b b)))
8.8b	(cbrt (fma a a (* b b)))
0.3b	(* (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
9×	`add-sqr-sqrt` `pow1` `-un-lft-identity` `associate-r*` `add-exp-log` `add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-l` `*-commutative`

Counts

4 → 67

Calls

4 calls:

Slowest

58.0ms	(* (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b)))))
6.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
1.0ms	(cbrt (fma a a (* b b)))
1.0ms	(cbrt (fma a a (* b b)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))
138.0ms	(cbrt (fma a a (* b b)))
124.0ms	(cbrt (fma a a (* b b)))
45.0ms	(* (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b)))))

simplify2.7s

Counts

35 → 79

Calls

35 calls:

Slowest

453.0ms	(* (* (* (fma a a (* b b)) (fma a a (* b b))) (* (* (sqrt (cbrt (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b)))))) (* (* (sqrt (cbrt (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b))))))
321.0ms	(* (* (* (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b)))))) (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b)))))) (* (* (sqrt (cbrt (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b))))))
215.0ms	(+ (+ (log (cbrt (* (fma a a (* b b)) (fma a a (* b b))))) (log (sqrt (cbrt (fma a a (* b b)))))) (log (sqrt (cbrt (fma a a (* b b))))))
211.0ms	(* (* (cbrt (* (fma a a (* b b)) (fma a a (* b b)))) (sqrt (cbrt (fma a a (* b b))))) (sqrt (cbrt (fma a a (* b b)))))
198.0ms	(cbrt (* (fma a a (* b b)) (fma a a (* b b))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.8s

20442×

body

valid