Details

Time bar (total: 6.5s)

sample53.0ms

Algorithm
intervals
Results
32.0ms644×body80valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213
done500213

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series323.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
55.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify47.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0391706
11680606
25002592
done5002592

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-exp-log
18×unpow-prod-down
15×add-cube-cbrt *-un-lft-identity
12×prod-exp
11×add-cbrt-cube
10×associate-*r* unswap-sqr sqr-pow
9×pow1
8×associate-*l*
7×swap-sqr
6×pow-to-exp prod-diff pow-exp
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
2×sub-neg associate-*r/ *-commutative fma-udef
1×pow2 flip3-- pow-sqr pow-prod-up flip--
Counts
4 → 107
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
18.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
56.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
164.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

simplify59.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04611208
120681035
250031014
done50031014

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
0.2b
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (fma a a (* b b)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log
69×prod-exp
34×pow-to-exp pow-exp
29×add-sqr-sqrt
20×associate-*r*
18×unpow-prod-down
16×add-cbrt-cube
15×add-cube-cbrt *-un-lft-identity
10×pow1 unswap-sqr
9×associate-*l* sqr-pow
7×cbrt-unprod
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative
2×sub-neg associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- fma-udef hypot-def
Counts
4 → 145
Calls
4 calls:
20.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
44.0ms
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(sqrt (fma a a (* b b)))

series696.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
259.0ms
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
46.0ms
(sqrt (fma a a (* b b)))

simplify88.0ms

Counts
157 → 157
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07491874
129201690
250011525
done50011525

prune606.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (fma a a (* b b)))
18.4b
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
18.4b
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
18.4b
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def
Counts
4 → 49
Calls
4 calls:
2.0ms
(sqrt (fma a a (* b b)))
28.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
26.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
29.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))

series902.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (fma a a (* b b)))
289.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
283.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))
283.0ms
(cbrt (* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2))))

simplify118.0ms

Counts
61 → 61
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
0155805
1347697
21238691
34611687
45002687
done5002687

prune479.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03424
13424
done3424

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s20599×body80valid