Details

Time bar (total: 37.8s)

sample203.0ms

Algorithm
intervals
Results
77.0ms821×body80nan
18.0ms191×body80valid
17.0ms15×body1280valid
12.0ms25×body640valid
6.0ms20×body320valid
2.0ms7×body160valid

simplify14.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
01417
12716
25716
313016
428116
564916
6137216
7248416
8332916
9355716
10356116
done356116

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.7b

localize19.0ms

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))
5.6b
(log (- 1.0 y))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
32×*-un-lft-identity
21×log-prod
20×add-cube-cbrt
11×pow1
10×associate-*l*
9×add-exp-log prod-diff add-log-exp
8×distribute-rgt-in distribute-lft-in associate-*r* add-cbrt-cube
6×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u flip3-- associate-*l/ flip-- log1p-expm1-u
3×fma-neg 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 → 114
Calls
4 calls:
29.0ms
(* (- z 1.0) (log (- 1.0 y)))
102.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
44.0ms
(* (- x 1.0) (log y))
7.0ms
(log (- 1.0 y))

series390.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (- z 1.0) (log (- 1.0 y)))
222.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
62.0ms
(* (- x 1.0) (log y))
46.0ms
(log (- 1.0 y))

simplify1.4s

Counts
126 → 126
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02632037
15871849
217801611
done50001495

prune459.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
80×times-frac
72×associate-*r*
71×*-un-lft-identity
67×add-cube-cbrt
56×unpow-prod-down
34×associate-+r+
33×prod-diff
29×add-exp-log
24×unpow2 sqr-pow
23×distribute-rgt-in distribute-lft-in
22×flip3-- associate-*l/ flip--
18×log-prod unswap-sqr
16×frac-add
15×pow1
11×prod-exp add-cbrt-cube add-log-exp
9×div-exp
8×frac-times associate-*l*
7×associate--l+ log-pow
6×pow-to-exp associate-+l+ pow-exp
5×associate-*r/
4×expm1-log1p-u log1p-expm1-u
3×sub-neg fma-neg cbrt-unprod
2×diff-log pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares
1×cbrt-undiv +-commutative fma-def flip3-+ flip-+ div-inv
Counts
4 → 243
Calls
4 calls:
109.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
37.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
44.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
32.0ms
(* (- x 1.0) (log y))

series675.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
215.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
70.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
73.0ms
(* (- x 1.0) (log y))

simplify826.0ms

Counts
255 → 255
Iterations

Useful iterations: done (817.0ms)

IterNodesCost
05647141
114646037
done50015472

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt y) (cbrt y))
0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)

rewrite16.0ms

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×expm1-log1p-u add-cbrt-cube log1p-expm1-u 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 → 81
Calls
4 calls:
11.0ms
(* (cbrt y) (cbrt y))
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)

series947.0ms

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (cbrt y) (cbrt y))
223.0ms
(cbrt y)
206.0ms
(cbrt y)
208.0ms
(cbrt y)

simplify4.8s

Counts
93 → 93
Iterations

Useful iterations: done (4.8s)

IterNodesCost
065554
1119443
2327423
31104405
44523400
done5001390

prune694.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- x 1.0) (log y))
9.5b
(+ (* (log (+ (sqrt 1.0) (sqrt y))) (- z 1.0)) (* (- z 1.0) (log (- (sqrt 1.0) (sqrt y)))))
11.6b
(log (+ (sqrt 1.0) (sqrt y)))
12.0b
(log (- (sqrt 1.0) (sqrt y)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
42×*-un-lft-identity
38×log-prod
24×add-cube-cbrt
23×distribute-rgt-in distribute-lft-in
22×associate-+l+
20×sqrt-prod
18×associate-+r+ prod-diff
13×difference-of-squares
9×pow1
8×add-exp-log
7×distribute-lft-out--
6×flip3-- associate-*l/ add-cbrt-cube flip-- add-log-exp
5×associate-*l*
4×expm1-log1p-u log-div associate-*r/ associate-*r* frac-add log1p-expm1-u
3×log-pow
2×sub-neg flip3-+ rem-log-exp flip-+ distribute-lft-out
1×+-commutative fma-def pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 129
Calls
4 calls:
24.0ms
(* (- x 1.0) (log y))
57.0ms
(+ (* (log (+ (sqrt 1.0) (sqrt y))) (- z 1.0)) (* (- z 1.0) (log (- (sqrt 1.0) (sqrt y)))))
15.0ms
(log (+ (sqrt 1.0) (sqrt y)))
21.0ms
(log (- (sqrt 1.0) (sqrt y)))

series1.1s

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- x 1.0) (log y))
540.0ms
(+ (* (log (+ (sqrt 1.0) (sqrt y))) (- z 1.0)) (* (- z 1.0) (log (- (sqrt 1.0) (sqrt y)))))
195.0ms
(log (+ (sqrt 1.0) (sqrt y)))
234.0ms
(log (- (sqrt 1.0) (sqrt y)))

simplify1.2s

Counts
141 → 141
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02912815
17422515
222302108
done50002100

prune926.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes406.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02539
12939
done2939

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.5s23761×body80nan
717.0ms5871×body80valid
479.0ms774×body640valid
279.0ms301×body1280valid
211.0ms676×body320valid
80.0ms421×body160valid