Details

Time bar (total: 50.5s)

sample124.0ms

Algorithm
intervals
Results
99.0ms604×body80valid

simplify197.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
196.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* b b) (+ 3 a))
0.3b
(pow (+ (* a a) (* b b)) 2)
0.0b
(* (* a a) (- 1 a))
0.0b
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
10×associate-*r*
8×fma-def
6×unpow-prod-down pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×pow-unpow
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unpow2 difference-of-squares unswap-sqr sqr-pow
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 121
Calls
4 calls:
Slowest
83.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
39.0ms
(* (* b b) (+ 3 a))
30.0ms
(* (* a a) (- 1 a))
9.0ms
(pow (+ (* a a) (* b b)) 2)

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
76.0ms
(* (* a a) (- 1 a))
54.0ms
(pow (+ (* a a) (* b b)) 2)
51.0ms
(* (* b b) (+ 3 a))

simplify9.6s

Counts
83 → 133
Calls
83 calls:
Slowest
745.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
656.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
454.0ms
(* (* (* b b) (+ 3 a)) 4)
372.0ms
(- (+ (* 4 (pow a 2)) (* 12 (pow b 2))) (* 4 (pow a 3)))
354.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* b b) (+ 3 a))
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)))

rewrite116.0ms

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
9×*-un-lft-identity
8×associate-*r*
7×add-cube-cbrt
5×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef unswap-sqr
2×distribute-rgt-in distribute-lft-in associate-*r/
1×flip3-+ swap-sqr flip-+ distribute-lft-out
Counts
4 → 127
Calls
4 calls:
Slowest
53.0ms
(* (* b b) (+ 3 a))
50.0ms
(* (* a a) (* a a))
11.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
99.0ms
(* b (fma b b (* 2 (* a a))))
50.0ms
(* (* b b) (+ 3 a))
44.0ms
(* (* a a) (* a a))

simplify5.6s

Counts
107 → 139
Calls
107 calls:
Slowest
870.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
418.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
329.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
314.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
311.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* b b) (+ 3 a))
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
(* (* a a) (- 1 a))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
25×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×pow1 add-cbrt-cube add-exp-log
13×distribute-rgt-in distribute-lft-in associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
5×associate-*l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative fma-udef unswap-sqr
2×sub-neg difference-of-squares
1×flip3-+ flip3-- flip-+ flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
Slowest
52.0ms
(* (* a a) (- 1 a))
51.0ms
(* (* b b) (+ 3 a))
13.0ms
(* b (fma b b (* 2 (* a a))))
0.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
72.0ms
(* (* a a) (- 1 a))
70.0ms
(* b (fma b b (* 2 (* a a))))
47.0ms
(* (* b b) (+ 3 a))

simplify7.4s

Counts
78 → 122
Calls
78 calls:
Slowest
877.0ms
(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
684.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
592.0ms
(* (* (* (* a a) a) (* (* a a) a)) (* (* (- 1 a) (- 1 a)) (- 1 a)))
292.0ms
(* (* (* (* b b) (* b b)) (* b b)) (* (* (+ 3 a) (+ 3 a)) (+ 3 a)))
253.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

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))))

rewrite12.0ms

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
9.0ms
(* (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)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(* (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))))
169.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
169.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))
165.0ms
(cbrt (fma b (* b (fma b b (* 2 (* a a)))) (pow a 4)))

simplify13.4s

Counts
65 → 97
Calls
65 calls:
Slowest
650.0ms
(* (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)))))
353.0ms
(* (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)))))
353.0ms
(* (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)))))
349.0ms
(* (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)))))
345.0ms
(* (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)))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.6s20149×body80valid