Details

Time bar (total: 33.6s)

sample296.0ms

Algorithm
intervals
Results
119.0ms784×body80nan
25.0ms186×body80valid
21.0ms26×body640valid
15.0ms11×body1280valid
11.0ms25×body320valid
3.0ms11×body160valid

simplify5.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12617
24917
311717
434617
5139117
6473117
done500017

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b
(* (- x 1.0) (log y))
5.8b
(log (- 1.0 y))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×*-un-lft-identity
21×log-prod
13×add-cube-cbrt
11×pow1
10×associate-*l*
9×add-exp-log add-log-exp
8×distribute-rgt-in distribute-lft-in associate-*r* add-cbrt-cube
6×distribute-lft-out-- difference-of-squares
4×flip3-- associate-*l/ flip--
3×log-pow
2×log-div diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-log-exp associate--l+ sum-log
Counts
4 → 94
Calls
4 calls:
61.0ms
(* (- z 1.0) (log (- 1.0 y)))
174.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
39.0ms
(* (- x 1.0) (log y))
9.0ms
(log (- 1.0 y))

series553.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (- z 1.0) (log (- 1.0 y)))
280.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
103.0ms
(* (- x 1.0) (log y))
91.0ms
(log (- 1.0 y))

simplify1.5s

Counts
106 → 106
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02311491
15311443
221491283
done50021265

prune887.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b
(* (- x 1.0) (log y))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt flip3-- flip--
25×*-un-lft-identity
24×log-prod associate-*l/
16×distribute-rgt-in add-cube-cbrt distribute-lft-in frac-add
13×associate--l+
12×frac-times
11×add-log-exp
10×pow1 associate-+r+ associate-*r* associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-+l+ associate-*r/
5×sub-neg distribute-lft-out--
4×difference-of-squares
2×diff-log pow-prod-down prod-exp sum-log log-pow *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ flip-+
Counts
4 → 129
Calls
4 calls:
140.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
154.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
57.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
40.0ms
(* (- x 1.0) (log y))

series917.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
423.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
260.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
113.0ms
(* (- x 1.0) (log y))

simplify693.0ms

Counts
141 → 141
Iterations

Useful iterations: done (683.0ms)

IterNodesCost
03195151
19254731
done50004578

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.1b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b
(* (- x 1.0) (log y))
0.4b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite603.0ms

Algorithm
rewrite-expression-head
Rules
98×associate-*l/
88×frac-times
84×flip3-- flip--
52×frac-add
31×flip3-+ flip-+
29×add-sqr-sqrt
27×*-un-lft-identity
26×associate-*r/
20×associate-*r*
16×pow1
13×add-exp-log add-cube-cbrt add-cbrt-cube
12×log-prod sqrt-prod
11×distribute-rgt-in distribute-lft-in associate-*l*
6×associate-+l+ add-log-exp difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
4×sub-neg associate-+r+
3×log-pow *-commutative distribute-lft-out
2×unswap-sqr
1×+-commutative sum-log
Counts
4 → 190
Calls
4 calls:
68.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
169.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
42.0ms
(* (- x 1.0) (log y))
298.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
758.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
275.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
100.0ms
(* (- x 1.0) (log y))
450.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify1.2s

Counts
202 → 202
Iterations

Useful iterations: done (1.1s)

IterNodesCost
051717630
1171813017
done500012639

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt y) (cbrt y))
0.7b
(cbrt y)
0.7b
(cbrt y)
0.7b
(cbrt y)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
19.0ms
(* (cbrt y) (cbrt y))
2.0ms
(cbrt y)
1.0ms
(cbrt y)
2.0ms
(cbrt y)

series1.6s

Counts
4 → 12
Calls
4 calls:
436.0ms
(* (cbrt y) (cbrt y))
395.0ms
(cbrt y)
379.0ms
(cbrt y)
353.0ms
(cbrt y)

simplify1.8s

Counts
85 → 85
Iterations

Useful iterations: done (1.8s)

IterNodesCost
061524
1139417
2735397
done5000383

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes858.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02942
13742
done3742

end0.0ms

sample9.0s

Algorithm
intervals
Results
4.3s23483×body80nan
997.0ms5871×body80valid
516.0ms747×body640valid
435.0ms734×body320valid
333.0ms252×body1280valid
109.0ms427×body160valid