Details

Time bar (total: 22.0s)

sample156.0ms

Algorithm
intervals
Results
110.0ms656×body80valid

simplify7.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune5.0ms

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)))

rewrite249.0ms

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:
121.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
65.0ms
(* (* a a) (+ 1.0 a))
20.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series451.0ms

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))))))
73.0ms
(* (* a a) (+ 1.0 a))
139.0ms
(pow (+ (* a a) (* b b)) 2.0)
76.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.7s

Counts
91 → 91
Iterations

Useful iterations: 2 (501.0ms)

IterNodesCost
01751540
14791431
218381287
done50001287

prune389.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite139.0ms

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:
15.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
66.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
28.0ms
(* 2 (* (pow a 2) (pow b 2)))
27.0ms
(* (pow a 2) (pow b 2))

series281.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
87.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
75.0ms
(* 2 (* (pow a 2) (pow b 2)))
53.0ms
(* (pow a 2) (pow b 2))

simplify1.3s

Counts
113 → 113
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01461649
13731431
212391245
done50001231

prune433.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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))

rewrite126.0ms

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:
6.0ms
(- 1.0 (* 3.0 a))
47.0ms
(* (* a a) (+ 1.0 a))
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
19.0ms
(* (pow a 2) (pow b 2))

series222.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- 1.0 (* 3.0 a))
77.0ms
(* (* a a) (+ 1.0 a))
69.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
39.0ms
(* (pow a 2) (pow b 2))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01771371
14461243
216291011
done5000999

prune516.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

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)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×pow1 add-sqr-sqrt *-un-lft-identity
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/ pow-exp
3×pow-unpow pow-pow
2×sub-neg associate-+r+ flip3-+ div-exp associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp rec-exp flip3-- pow-flip 1-exp sum-log flip-- div-inv distribute-lft-out inv-pow sqr-pow
Counts
4 → 94
Calls
4 calls:
48.0ms
(+ (pow (/ 1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
64.0ms
(* (* a a) (+ 1.0 a))
14.0ms
(pow (/ 1 a) -4.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (pow (/ 1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
82.0ms
(* (* a a) (+ 1.0 a))
301.0ms
(pow (/ 1 a) -4.0)
73.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.5s

Counts
106 → 106
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02211530
15741403
219351253
done50001252

prune422.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

40.6% (1.3b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 2.3b

bsearch329.0ms

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

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
03695
15070
done5070

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.4s20728×body80valid