Details

Time bar (total: 20.3s)

sample98.0ms

Algorithm
intervals
Results
66.0ms693×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
15129
215429
345529
4168129
done500129

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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)
1.5b
(* (* b b) (+ 3.0 a))

rewrite259.0ms

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:
118.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
66.0ms
(* (* a a) (- 1.0 a))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (+ 3.0 a))

series546.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
87.0ms
(* (* a a) (- 1.0 a))
179.0ms
(pow (+ (* a a) (* b b)) 2.0)
72.0ms
(* (* b b) (+ 3.0 a))

simplify3.3s

Counts
93 → 93
Iterations

Useful iterations: 2 (970.0ms)

IterNodesCost
01791446
15591337
238321209
done50001209

prune449.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (pow (+ (* a a) (* b b)) 2.0))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.5b
(* (* b b) (+ 3.0 a))

rewrite188.0ms

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-+l+ 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:
82.0ms
(+ (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (pow (+ (* a a) (* b b)) 2.0))
41.0ms
(* (* a a) (- 1.0 a))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (+ 3.0 a))

series834.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(+ (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (pow (+ (* a a) (* b b)) 2.0))
487.0ms
(* (* a a) (- 1.0 a))
145.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (+ 3.0 a))

simplify3.1s

Counts
93 → 93
Iterations

Useful iterations: 2 (837.0ms)

IterNodesCost
01791446
15591353
238311225
done50011225

prune374.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* b b) (+ 3.0 a))
8.1b
(cbrt (+ (* a a) (* b b)))
8.1b
(cbrt (+ (* a a) (* b b)))
8.1b
(cbrt (+ (* a a) (* b b)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
41.0ms
(* (* b b) (+ 3.0 a))
11.0ms
(cbrt (+ (* a a) (* b b)))
22.0ms
(cbrt (+ (* a a) (* b b)))
9.0ms
(cbrt (+ (* a a) (* b b)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* b b) (+ 3.0 a))
150.0ms
(cbrt (+ (* a a) (* b b)))
173.0ms
(cbrt (+ (* a a) (* b b)))
139.0ms
(cbrt (+ (* a a) (* b b)))

simplify2.0s

Counts
75 → 75
Iterations

Useful iterations: done (2.0s)

IterNodesCost
097978
1297917
22163803
done5000794

prune568.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.2b
(* (pow a 2) (pow b 2))

rewrite195.0ms

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:
67.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
35.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
50.0ms
(* 2 (* (pow a 2) (pow b 2)))
36.0ms
(* (pow a 2) (pow b 2))

series258.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
78.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
56.0ms
(* 2 (* (pow a 2) (pow b 2)))
63.0ms
(* (pow a 2) (pow b 2))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01461649
13861443
224091247
done50001233

prune328.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes101.0ms

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
01829
12529
done2529

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.6s20552×body80valid