Details

Time bar (total: 1.5m)

sample54.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
10.0ms256×pre80true

simplify612.0ms

Counts
1 → 1
Iterations
IterNodes
42152
3441
2102
135
015

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ beta alpha))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite944.0ms

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×distribute-lft-out
778×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1217
Calls
4 calls:
14.0ms
(+ (* alpha beta) (+ beta alpha))
247.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
395.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
208.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series548.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* alpha beta) (+ beta alpha))
195.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
210.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
117.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify1.8s

Counts
1229 → 1229
Iterations
IterNodes
24340
11440
0611

prune14.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ beta alpha))
0.1b
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
0.1b
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite631.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
68×times-frac
60×add-exp-log
59×distribute-lft-out
53×add-sqr-sqrt
36×add-cbrt-cube add-cube-cbrt
26×div-exp associate-*l*
21×associate-*r*
16×prod-exp
14×cbrt-undiv
11×associate-/r*
9×add-log-exp
8×associate-/r/ cbrt-unprod
6×pow1 flip3-+ flip-+ unswap-sqr associate-/l/
5×associate-/l*
4×rec-exp 1-exp insert-posit16 div-inv
3×sum-log
2×frac-times clear-num frac-2neg associate-*l/ associate-*r/ un-div-inv
1×+-commutative associate-+r+ pow-prod-down *-commutative
Counts
4 → 183
Calls
4 calls:
13.0ms
(+ (* alpha beta) (+ beta alpha))
271.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
171.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
170.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series554.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (* alpha beta) (+ beta alpha))
206.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
221.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
110.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify1.2s

Counts
195 → 195
Iterations
IterNodes
23283
1827
0266

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta))))
0.0b
(* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
0.3b
(/ 1 (* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta))))
2.2b
(/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
1111×*-un-lft-identity
598×times-frac
563×distribute-lft-out
211×add-sqr-sqrt
202×add-cube-cbrt
161×associate-*l*
54×add-exp-log
35×associate-/r/
34×add-cbrt-cube
32×associate-/r*
24×div-exp
20×flip3-+ flip-+
17×div-inv
14×cbrt-undiv
13×associate-/l*
12×prod-exp
9×pow1
6×cbrt-unprod
5×associate-*r*
4×frac-times rec-exp 1-exp associate-*r/ insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg unswap-sqr
2×pow-prod-down associate-*l/ pow-flip
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 486
Calls
4 calls:
187.0ms
(/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta))))
396.0ms
(* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
227.0ms
(/ 1 (* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta))))
178.0ms
(/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))

series785.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta))))
320.0ms
(* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
199.0ms
(/ 1 (* (/ (+ 1.0 (+ 2 (+ alpha beta))) (/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta))))
93.0ms
(/ (+ 1.0 (+ (* beta alpha) (+ alpha beta))) (+ 2 (+ alpha beta)))

simplify2.6s

Counts
498 → 498
Iterations
IterNodes
25459
11378
0369

prune5.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) 1) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
0.6b
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
2.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
8114×*-un-lft-identity
6138×times-frac
3736×distribute-lft-out
3544×sqrt-prod
1994×add-sqr-sqrt add-cube-cbrt
250×associate-/l*
188×associate-/r/
104×div-inv
96×flip3-+ flip-+
28×associate-/r*
20×add-exp-log
18×add-cbrt-cube
10×div-exp
8×cbrt-undiv
6×associate-/l/
4×pow1 clear-num frac-2neg sqrt-div insert-posit16 add-log-exp
1×1-exp
Counts
4 → 2567
Calls
4 calls:
273.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) 1) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
333.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
197.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
190.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series1.2s

Counts
4 → 12
Calls
4 calls:
239.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) 1) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
212.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (sqrt (+ (+ (+ alpha 2) beta) 1.0)))
119.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
600.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify3.5s

Counts
2579 → 2579
Iterations
IterNodes
13085
01347

prune46.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

69.2% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 3.5b

bsearch133.0ms

Steps
ItersRangePoint
8
2.2761248815143707e+155
8.433679759694109e+157
2.5246833345897584e+155

simplify5.0ms

Iterations
IterNodes
240
140
027

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8000×body80valid
271.0ms8000×pre80true