Details

sample174.0ms

Algorithm

intervals

Results

144.0ms

626×

body

valid

simplify184.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

184.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize68.0ms

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)

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

series439.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(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))
129.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
121.0ms	(fma (* a a) a (* a a))
42.0ms	(fma -3 a 1)

simplify1.3s

Counts

12 → 56

Calls

12 calls:

Slowest

272.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
271.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
253.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
228.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
136.0ms	(- (+ (* 4 (pow a 2)) (* 4 (pow b 2))) 1)

prune839.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

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`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series419.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(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))
104.0ms	(fma (* a a) a (* a a))
89.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
68.0ms	(fma -3 a 1)

simplify1.5s

Counts

12 → 56

Calls

12 calls:

Slowest

351.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
300.0ms	(+ (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)))
274.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
126.0ms	(- (+ (* 4 (pow a 2)) (* 4 (pow b 2))) 1)

prune832.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(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	(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	(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	(* (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))))

rewrite22.0ms

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

16.0ms	(* (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))) (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)))
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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

319.0ms	(* (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))) (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))))
315.0ms	(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)))
291.0ms	(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)))
289.0ms	(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)))

simplify14.0s

Counts

65 → 97

Calls

65 calls:

Slowest

615.0ms	(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)))
526.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
491.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
443.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
437.0ms	(* (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)) (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)))

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(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	(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	(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	(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)))

rewrite7.0ms

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`

Counts

4 → 56

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)))
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)))
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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

317.0ms	(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)))
298.0ms	(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)))
296.0ms	(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)))
293.0ms	(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)))

simplify5.2s

Counts

24 → 68

Calls

24 calls:

Slowest

519.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
454.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
446.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
433.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
295.0ms	(+ (* 4/3 (pow (/ 1 (pow b 2)) 1/3)) (pow (/ -1 b) -4/3))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes207.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

4.1s

20385×

body

valid