Details

Time bar (total: 11.7s)

sample56.0ms

Algorithm
intervals
Results
37.0ms691×body80valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
214031
334431
484131
5185531
6375331
done500031

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite60.0ms

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:
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
116.0ms
(pow (+ (* a a) (* b b)) 2.0)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify910.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (326.0ms)

IterNodesCost
01751540
14901431
220021287
done50001287

prune268.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite84.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
189.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
190.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify562.0ms

Counts
92 → 92
Iterations

Useful iterations: done (558.0ms)

IterNodesCost
01202304
13292090
212511892
done50011888

prune350.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
9×add-exp-log sqrt-prod add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
14.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
31.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
193.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
188.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify575.0ms

Counts
82 → 82
Iterations

Useful iterations: done (572.0ms)

IterNodesCost
01202710
13292399
212512234
done50012228

prune389.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.3b
(* (pow a 2) (pow b 2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
15.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series137.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
45.0ms
(* 2 (* (pow a 2) (pow b 2)))
35.0ms
(* (pow a 2) (pow b 2))

simplify660.0ms

Counts
96 → 96
Iterations

Useful iterations: done (657.0ms)

IterNodesCost
01221229
12981062
21208884
done5000882

prune220.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02396
13296
done3296

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s21017×body80valid