Details

Time bar (total: 18.6s)

sample122.0ms

Algorithm
intervals
Results
93.0ms656×body80valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite136.0ms

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:
58.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
31.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
66.0ms
(* (* a a) (+ 1.0 a))
156.0ms
(pow (+ (* a a) (* b b)) 2.0)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.2s

Counts
91 → 91
Iterations

Useful iterations: 2 (396.0ms)

IterNodesCost
01751540
14791431
218381287
done50001287

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))
2.3b
(* (pow a 2) (pow b 2))

rewrite105.0ms

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:
13.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
40.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
25.0ms
(* 2 (* (pow a 2) (pow b 2)))
23.0ms
(* (pow a 2) (pow b 2))

series252.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
75.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
49.0ms
(* 2 (* (pow a 2) (pow b 2)))
39.0ms
(* (pow a 2) (pow b 2))

simplify945.0ms

Counts
113 → 113
Iterations

Useful iterations: done (941.0ms)

IterNodesCost
01461649
13731431
212391245
done50001231

prune300.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
2.3b
(* (pow a 2) (pow b 2))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
18×unswap-sqr
16×add-cbrt-cube
15×associate-*r* prod-exp
14×pow1 unpow-prod-down
12×*-un-lft-identity
10×add-cube-cbrt associate-*l* unpow2 sqr-pow
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×associate-*r/
3×distribute-rgt-in sub-neg distribute-lft-in *-commutative
2×flip3-- flip--
1×flip3-+ diff-log flip-+ distribute-lft-out
Counts
4 → 112
Calls
4 calls:
7.0ms
(- 1.0 (* 3.0 a))
55.0ms
(* (* a a) (+ 1.0 a))
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
37.0ms
(* (pow a 2) (pow b 2))

series232.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- 1.0 (* 3.0 a))
81.0ms
(* (* a a) (+ 1.0 a))
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
45.0ms
(* (pow a 2) (pow b 2))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01771371
14461243
216291011
done5000999

prune511.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (/ -1 a) -4.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
16×add-sqr-sqrt *-un-lft-identity
15×pow1
14×add-cube-cbrt add-cbrt-cube
13×unpow-prod-down
9×times-frac
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* pow-exp *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow div-exp sum-log flip-- div-inv distribute-lft-out sqr-pow
Counts
4 → 90
Calls
4 calls:
66.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(pow (/ -1 a) -4.0)
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
70.0ms
(* (* a a) (+ 1.0 a))
272.0ms
(pow (/ -1 a) -4.0)
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: 2 (462.0ms)

IterNodesCost
02151522
15631427
219851267
done50021267

prune433.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

33.5% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 2.3b

bsearch286.0ms

Steps
ItersRangePoint
7
3.744599964535267e-06
8.937283511995443e-05
8.82997045828262e-05
10
-50.53194642688064
-2.0220103258854106e-10
-0.0031084792160490805

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
039153
15399
done5399

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.6s20728×body80valid