Details

Time bar (total: 40.9s)

sample84.0ms

Algorithm
intervals
Results
65.0ms604×body80valid

simplify179.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
179.0ms
(- (+ (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

localize20.0ms

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
87.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
14.0ms
(+ (* a a) (* b b))
14.0ms
(* 4 (* b b))
8.0ms
(pow (+ (* a a) (* b b)) 2)

series213.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
60.0ms
(pow (+ (* a a) (* b b)) 2)
37.0ms
(* 4 (* b b))
32.0ms
(+ (* a a) (* b b))

simplify4.1s

Counts
38 → 92
Calls
38 calls:
Slowest
339.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
322.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
303.0ms
(pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2)
276.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
270.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune961.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

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))

rewrite68.0ms

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
40.0ms
(* (* a a) (* a a))
18.0ms
(* 4 (* b b))
5.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
103.0ms
(* b (fma b b (* 2 (* a a))))
68.0ms
(* (* a a) (* a a))
47.0ms
(* 4 (* b b))

simplify5.4s

Counts
101 → 134
Calls
101 calls:
Slowest
825.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
369.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
354.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
348.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
342.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

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
(* 2 (* a a))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-cbrt-cube add-exp-log
12×add-sqr-sqrt
9×associate-*l*
8×*-un-lft-identity add-cube-cbrt
7×pow-prod-down prod-exp cbrt-unprod
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
Counts
4 → 78
Calls
4 calls:
Slowest
34.0ms
(* 2 (* a a))
26.0ms
(* 4 (* b b))
11.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
79.0ms
(* b (fma b b (* 2 (* a a))))
42.0ms
(* 4 (* b b))
27.0ms
(* 2 (* a a))

simplify4.4s

Counts
44 → 90
Calls
44 calls:
Slowest
846.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
649.0ms
(* (* (* 4 4) 4) (* (* (* b b) (* b b)) (* b b)))
295.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
271.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
266.0ms
(* (* (* 2 2) 2) (* (* (* a a) (* a a)) (* a a)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

22.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
22.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
22.9b
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
0.4b
(* (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))))

rewrite10.0ms

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
7.0ms
(* (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))))
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)))
1.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
177.0ms
(* (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))))
177.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
160.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))

simplify15.7s

Counts
65 → 97
Calls
65 calls:
Slowest
463.0ms
(* (cbrt (sqrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))) (sqrt (cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))))
431.0ms
(* (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)))))
426.0ms
(* (sqrt (cbrt (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)))))
424.0ms
(cbrt (* (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)))))
419.0ms
(* (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)))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.2s20149×body80valid