Details

Time bar (total: 20.3s)

sample81.0ms

Algorithm
intervals
Results
50.0ms655×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216131
348631
4164531
done500131

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
93.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
64.0ms
(* (* a a) (+ 1.0 a))
32.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
83.0ms
(* (* a a) (+ 1.0 a))
175.0ms
(pow (+ (* a a) (* b b)) 2.0)
67.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.4s

Counts
91 → 91
Iterations

Useful iterations: 2 (898.0ms)

IterNodesCost
01751540
15511441
238261287
done50001287

prune390.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
44.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
92.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
717.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
208.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01202304
13422090
219001900
done50021892

prune583.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.5b
(* (pow a 2) (pow b 2))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
27.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
72.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
51.0ms
(* 2 (* (pow a 2) (pow b 2)))
34.0ms
(* (pow a 2) (pow b 2))

series303.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
74.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
68.0ms
(* 2 (* (pow a 2) (pow b 2)))
66.0ms
(* (pow a 2) (pow b 2))

simplify2.2s

Counts
113 → 113
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01461649
13861443
224081245
done50011237

prune442.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
25.4b
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) 3))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
15×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity sqrt-prod
11×pow1
9×add-exp-log add-cbrt-cube
6×unpow-prod-down sqrt-div cube-prod
4×add-log-exp
3×flip3-+ associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×cube-div distribute-rgt-in sub-neg rem-sqrt-square cbrt-div distribute-lft-in sqrt-pow1 pow1/2 associate-*r/
1×cube-mult flip3-- pow1/3 unpow3 associate-*l* *-commutative flip-- rem-cbrt-cube unswap-sqr sqr-pow
Counts
4 → 84
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
83.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
98.0ms
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) 3))

series762.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
228.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
223.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
242.0ms
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) 3))

simplify1.9s

Counts
96 → 96
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01593843
14673026
228392949
done50022945

prune517.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes312.0ms

Accuracy

98.3% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.4b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03685
14885
done4885

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.7s20583×body80valid