Details

Time bar (total: 41.0s)

sample96.0ms

Algorithm
intervals
Results
79.0ms664×body80valid

simplify217.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
217.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2)
0.0b
(* 4 (* b b))
0.0b
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b
(+ (* a a) (* b b))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 add-exp-log
9×fma-def *-un-lft-identity add-cbrt-cube add-cube-cbrt
8×add-log-exp
6×unpow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative sum-log flip3-+ flip-+ unpow2 sqr-pow
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr
Counts
4 → 80
Calls
4 calls:
Slowest
79.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
15.0ms
(+ (* a a) (* b b))
14.0ms
(pow (+ (* a a) (* b b)) 2)
14.0ms
(* 4 (* b b))

series211.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
54.0ms
(pow (+ (* a a) (* b b)) 2)
39.0ms
(* 4 (* b b))
37.0ms
(+ (* a a) (* b b))

simplify4.0s

Counts
38 → 92
Calls
38 calls:
Slowest
329.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
285.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
276.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
272.0ms
(+ (* 2 (* (pow a 2) (pow b 2))) (+ (* 4 (pow b 2)) (pow a 4)))
271.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2)) (cbrt (pow (+ (* a a) (* b b)) 2)))

prune881.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a a) (* a a))
0.2b
(* b (fma b b (* 2 (* a a))))
0.1b
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
0.0b
(* 4 (* b b))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
122×pow1
36×pow-prod-up
27×pow-prod-down
23×add-cbrt-cube add-exp-log
22×pow-sqr
18×pow-plus
13×pow2
12×prod-exp cbrt-unprod
10×add-sqr-sqrt
7×*-un-lft-identity associate-*l* add-cube-cbrt
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in swap-sqr
Counts
4 → 122
Calls
4 calls:
Slowest
54.0ms
(* (* a a) (* a a))
21.0ms
(* 4 (* b b))
11.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
75.0ms
(* b (fma b b (* 2 (* a a))))
39.0ms
(* 4 (* b b))
35.0ms
(* (* a a) (* a a))

simplify5.2s

Counts
101 → 134
Calls
101 calls:
Slowest
776.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
424.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
340.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
326.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) a) (* (* a a) a)))
326.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* b (fma b b (* 2 (* a a))))
0.1b
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
0.0b
(* 4 (* b b))
0.0b
(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (* b b)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
8×*-un-lft-identity add-cube-cbrt
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod fma-udef insert-posit16 log1p-expm1-u
3×fma-def
2×*-commutative unswap-sqr
1×distribute-rgt-in +-commutative associate-+l+ sum-log distribute-lft-in flip3-+ flip-+
Counts
4 → 74
Calls
4 calls:
Slowest
13.0ms
(* 4 (* b b))
12.0ms
(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (* b b)))
6.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series317.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(+ (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)) (* 4 (* b b)))
86.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
78.0ms
(* b (fma b b (* 2 (* a a))))
34.0ms
(* 4 (* b b))

simplify5.2s

Counts
38 → 86
Calls
38 calls:
Slowest
792.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
418.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (* 4 (pow b 2))))
363.0ms
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))
346.0ms
(sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
309.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

20.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
20.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
20.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
0.3b
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))

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
16.0ms
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))
2.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
1.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
1.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
562.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
217.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
216.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
212.0ms
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))

simplify14.7s

Counts
65 → 97
Calls
65 calls:
Slowest
431.0ms
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))
422.0ms
(* (cbrt (sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))) (cbrt (sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))))
403.0ms
(* (cbrt (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))) (cbrt (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))))
402.0ms
(* (cbrt (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))) (cbrt (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))))
402.0ms
(* (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))) (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes365.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.1s20881×body80valid