Details

Time bar (total: 19.6s)

sample112.0ms

Algorithm
intervals
Results
73.0ms669×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
215429
345529
4168129
done500129

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
76.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
48.0ms
(* (* a a) (- 1.0 a))
18.0ms
(pow (+ (* a a) (* b b)) 2.0)
41.0ms
(* (* b b) (+ 3.0 a))

series443.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
90.0ms
(* (* a a) (- 1.0 a))
153.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (+ 3.0 a))

simplify3.7s

Counts
93 → 93
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
01791446
15591337
238321209
done50001209

prune443.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize15.0ms

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)))
2.1b
(* (pow a 2) (pow b 2))

rewrite67.0ms

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:
14.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
31.0ms
(* 2 (* (pow a 2) (pow b 2)))
18.0ms
(* (pow a 2) (pow b 2))

series165.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
53.0ms
(* 2 (* (pow a 2) (pow b 2)))
39.0ms
(* (pow a 2) (pow b 2))

simplify1.6s

Counts
96 → 96
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01221229
13091074
21948886
done5000876

prune371.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 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))
2.1b
(* (pow a 2) (pow b 2))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×add-exp-log
20×associate-*r*
19×unswap-sqr
18×associate-*r/ add-cbrt-cube
16×pow1 *-un-lft-identity prod-exp
14×unpow-prod-down
13×associate-*l*
12×add-cube-cbrt
10×unpow2 sqr-pow
8×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×distribute-rgt-in distribute-lft-in flip3-+ frac-add *-commutative flip-+ add-log-exp
3×flip3-- flip--
2×sub-neg
1×distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 128
Calls
4 calls:
107.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
49.0ms
(* (* a a) (- 1.0 a))
51.0ms
(* (* b b) (+ 3.0 a))
18.0ms
(* (pow a 2) (pow b 2))

series279.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
88.0ms
(* (* a a) (- 1.0 a))
57.0ms
(* (* b b) (+ 3.0 a))
43.0ms
(* (pow a 2) (pow b 2))

simplify510.0ms

Counts
140 → 140
Iterations

Useful iterations: done (504.0ms)

IterNodesCost
02431906
17581748
done50001476

prune625.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3.0 a))
0.5b
(* (* b b) (+ 3.0 a))
3.6b
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
32.6b
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite502.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
21×*-un-lft-identity
18×times-frac
17×add-cube-cbrt
16×add-exp-log add-cbrt-cube
15×difference-of-squares
14×pow1
8×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
5×unpow-prod-down sqr-pow
4×associate-*r/ associate--r+
3×flip3-- associate-/r* flip--
2×flip3-+ associate-*l* associate-/r/ *-commutative flip-+ associate-/l/ distribute-lft-out unswap-sqr
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 111
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
41.0ms
(* (* b b) (+ 3.0 a))
132.0ms
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
293.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (* b b) (+ 3.0 a))
59.0ms
(* (* b b) (+ 3.0 a))
995.0ms
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
536.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify2.7s

Counts
123 → 123
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02156827
16276613
237726043
done50006041

prune613.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes225.0ms

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
2.9s20565×body80valid