Details

Time bar (total: 1.2m)

sample68.0ms

Algorithm
intervals
Results
23.0ms130×body80valid
18.0ms53×body1280valid
12.0ms42×body640valid
4.0ms20×body320valid
1.0ms11×body160valid

simplify158.0ms

Counts
1 → 1
Iterations
IterNodes
done168
15168
14165
13136
12114
1199
1089
969
853
742
632
526
423
322
219
115
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))
2.7b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
244×*-un-lft-identity
160×frac-sub
149×add-sqr-sqrt
145×associate-/r*
95×associate-/l*
77×add-cube-cbrt
60×times-frac
46×distribute-lft-out
34×difference-of-squares
28×clear-num frac-2neg distribute-lft-out--
22×associate-/l/
15×difference-of-sqr-1
12×flip3-+ flip-+
7×add-cbrt-cube add-exp-log
5×add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv flip3-- div-exp div-inv flip--
1×sub-neg diff-log
Counts
3 → 276
Calls
3 calls:
44.0ms
(/ (+ x 1) (- x 1))
21.0ms
(/ x (+ x 1))
175.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(/ (+ x 1) (- x 1))
30.0ms
(/ x (+ x 1))
91.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.9s

Counts
285 → 285
Iterations
IterNodes
done5001
11826
0521

prune902.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ 1 (- x 1))
0.1b
(* (+ x 1) (/ 1 (- x 1)))
3.9b
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
440×frac-sub
430×*-un-lft-identity
418×associate-/r*
386×add-sqr-sqrt
286×frac-times
248×associate-/l*
191×add-cube-cbrt
155×flip3-+ flip-+
143×associate-*r/
90×clear-num
88×difference-of-squares
79×frac-2neg
64×times-frac
50×distribute-lft-out
43×distribute-lft-out--
40×difference-of-sqr-1
33×un-div-inv
27×associate-*r*
22×associate-*l/
19×add-exp-log
13×add-cbrt-cube
9×unswap-sqr
7×pow1
6×associate-*l* associate-/r/ add-log-exp
5×div-exp
4×prod-exp insert-posit16
3×cbrt-undiv flip3-- div-inv flip--
2×rec-exp 1-exp cbrt-unprod
1×sub-neg diff-log pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 642
Calls
4 calls:
10.0ms
(/ x (+ x 1))
12.0ms
(/ 1 (- x 1))
73.0ms
(* (+ x 1) (/ 1 (- x 1)))
273.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ x (+ x 1))
15.0ms
(/ 1 (- x 1))
31.0ms
(* (+ x 1) (/ 1 (- x 1)))
115.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

simplify3.0s

Counts
654 → 654
Iterations
IterNodes
done5001
14397
01171

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(/ x (sqrt (+ 1 x)))
6.9b
(/ (- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x)))) (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
12.3b
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

rewrite13.2s

Algorithm
rewrite-expression-head
Rules
2020×sqrt-div
1974×associate-*l/
1948×frac-times
1901×*-un-lft-identity
1773×flip3-+ flip-+
1517×add-sqr-sqrt
1500×frac-sub
1014×associate-*l*
1000×frac-add
799×associate-/r*
752×associate-/l/
709×times-frac
594×sqrt-prod
515×flip3-- flip--
495×add-cube-cbrt
430×distribute-lft-out
399×unswap-sqr
396×distribute-lft-out--
344×associate-/l*
258×associate-*r*
226×difference-of-squares
110×clear-num frac-2neg
104×associate-*r/
40×*-commutative
28×associate-/r/
23×pow1
20×add-cbrt-cube add-exp-log
18×difference-of-sqr-1
9×add-log-exp
8×associate--l+
6×pow-plus prod-exp pow-prod-up cbrt-unprod
4×distribute-rgt-in cbrt-undiv +-commutative associate-+r+ distribute-lft-in swap-sqr div-exp insert-posit16 associate--r+
3×sub-neg div-sub pow-prod-down
2×pow2 diff-log pow3 pow-sqr div-inv
1×sum-log
Counts
4 → 2345
Calls
4 calls:
34.0ms
(* (* x x) x)
12.0ms
(/ x (sqrt (+ 1 x)))
8.9s
(/ (- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x)))) (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
3.9s
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* x x) x)
85.0ms
(/ x (sqrt (+ 1 x)))
626.0ms
(/ (- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x)))) (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
339.0ms
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

simplify5.8s

Counts
2357 → 2357
Iterations
IterNodes
done5001
03558

prune17.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

8.5b
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
8.5b
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
8.5b
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
12.3b
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

rewrite5.1s

Algorithm
rewrite-expression-head
Rules
1054×sqrt-div
1044×frac-times
1022×associate-*l/
931×flip3-+ flip-+
750×frac-sub
500×frac-add
378×associate-/r*
361×*-un-lft-identity
280×flip3-- flip--
251×add-sqr-sqrt
235×sqrt-prod
184×add-cube-cbrt
162×associate-/l*
108×cbrt-prod
102×associate-*l*
78×cbrt-div
75×distribute-lft-out
72×associate-*r/
54×clear-num frac-2neg
42×associate-*r*
28×unswap-sqr
18×distribute-lft-out--
11×difference-of-squares
9×add-log-exp
8×associate--l+
6×*-commutative
4×distribute-rgt-in pow1 associate-+r+ distribute-lft-in add-cbrt-cube add-exp-log insert-posit16
3×+-commutative sub-neg pow1/3 difference-of-sqr-1
2×times-frac diff-log associate--r+
1×sum-log
Counts
4 → 1001
Calls
4 calls:
336.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
362.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
342.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
3.8s
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

series864.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
183.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
202.0ms
(cbrt (* (* (sqrt (+ 1 x)) (- x 1)) (+ (* x x) (- 1 x))))
322.0ms
(- (* (* (/ x (sqrt (+ 1 x))) (- x 1)) (+ (* x x) (- 1 x))) (+ (* (sqrt (+ 1 x)) (* (* x x) x)) (sqrt (+ 1 x))))

simplify5.5s

Counts
1013 → 1013
Iterations
IterNodes
done5000
02728

prune8.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.2b

bsearch198.0ms

Steps
ItersRangePoint
7
12461.173664998358
2484744.5477507794
13687.362331495488
9
-101227.54480913779
-5.532094628653386e-05
-1.008231828666988

simplify42.0ms

Iterations
IterNodes
done81
381
277
169
045

end0.0ms

sample2.4s

Algorithm
intervals
Results
904.0ms1648×body1280valid
751.0ms4189×body80valid
412.0ms1207×body640valid
152.0ms624×body320valid
80.0ms332×body160valid