Details

Time bar (total: 15.4s)

sample90.0ms

Algorithm
intervals
Results
60.0ms653×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01829
15327
217226
355426
4211326
done500126

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
26×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
9×associate-*r*
7×fma-def
6×unpow-prod-down pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
115.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
57.0ms
(* (* a a) (- 1.0 a))
14.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (+ 3.0 a))

series475.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
86.0ms
(* (* a a) (- 1.0 a))
155.0ms
(pow (+ (* a a) (* b b)) 2.0)
44.0ms
(* (* b b) (+ 3.0 a))

simplify660.0ms

Counts
126 → 126
Iterations

Useful iterations: done (651.0ms)

IterNodesCost
02352118
17461794
done50001553

prune607.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2 (* a a))
1.1b
(fma (* 2 (* a a)) (* b b) (pow b 4))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×associate-*r* *-commutative fma-udef unswap-sqr
Counts
2 → 31
Calls
2 calls:
45.0ms
(* 2 (* a a))
1.0ms
(fma (* 2 (* a a)) (* b b) (pow b 4))

series139.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(* 2 (* a a))
110.0ms
(fma (* 2 (* a a)) (* b b) (pow b 4))

simplify560.0ms

Counts
37 → 37
Iterations

Useful iterations: 2 (144.0ms)

IterNodesCost
054378
1134365
2769318
done5000318

prune131.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 2.0 (* (pow a 2) (pow b 2)) (pow b 4)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.5b
(* (* b b) (+ 3.0 a))
1.7b
(* (pow a 2) (pow b 2))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
27×*-un-lft-identity
26×add-exp-log
23×add-cube-cbrt
18×prod-diff unswap-sqr
17×associate-*r*
16×add-cbrt-cube
15×prod-exp
14×pow1 unpow-prod-down
13×distribute-rgt-in distribute-lft-in
10×associate-*l* unpow2 sqr-pow
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def *-commutative
2×sub-neg associate-+r+ flip3-+ flip-+
1×+-commutative associate-+l+ flip3-- sum-log flip-- fma-udef distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 145
Calls
4 calls:
20.0ms
(+ (fma 2.0 (* (pow a 2) (pow b 2)) (pow b 4)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
64.0ms
(* (* a a) (- 1.0 a))
41.0ms
(* (* b b) (+ 3.0 a))
20.0ms
(* (pow a 2) (pow b 2))

series340.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(+ (fma 2.0 (* (pow a 2) (pow b 2)) (pow b 4)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
86.0ms
(* (* a a) (- 1.0 a))
44.0ms
(* (* b b) (+ 3.0 a))
39.0ms
(* (pow a 2) (pow b 2))

simplify596.0ms

Counts
157 → 157
Iterations

Useful iterations: done (588.0ms)

IterNodesCost
02692538
18142205
done50001877

prune720.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3)
0.3b
(pow (fma a a (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))
32.4b
(cbrt (pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp cbrt-unprod sqr-pow
2×cube-mult pow-to-exp pow-pow unpow3 associate-*r/ pow-exp
1×distribute-rgt-in distribute-lft-in flip3-+ pow1/3 associate-*l* *-commutative rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 93
Calls
4 calls:
16.0ms
(pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3)
5.0ms
(pow (fma a a (* b b)) 2.0)
53.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(cbrt (pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3))

series775.0ms

Counts
4 → 12
Calls
4 calls:
431.0ms
(pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3)
150.0ms
(pow (fma a a (* b b)) 2.0)
40.0ms
(* (* b b) (+ 3.0 a))
153.0ms
(cbrt (pow (fma (fma (pow a 2) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0 (pow (fma a a (* b b)) 2.0)) 3))

simplify2.2s

Counts
105 → 105
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01852687
15252434
234162098
done50002096

prune797.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
12529
done2529

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.8s20608×body80valid