Details

Time bar (total: 19.8s)

sample174.0ms

Algorithm
intervals
Results
72.0ms799×body80nan
15.0ms186×body80valid
11.0ms28×body640valid
9.0ms11×body1280valid
5.0ms23×body320valid
2.0ms11×body160valid

simplify288.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01213
12212
23812
35212
46012
57712
610512
715412
819812
922112
1023912
1124012
done24012

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (log (- 1.0 y)))
0.3b
(* x (log y))
4.5b
(log (- 1.0 y))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×log-prod
18×*-un-lft-identity
12×add-cube-cbrt
10×pow1
8×add-exp-log distribute-rgt-in distribute-lft-in associate-*r*
7×add-cbrt-cube
6×associate-*l*
3×expm1-log1p-u log-pow log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
2×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- rem-log-exp flip--
Counts
3 → 76
Calls
3 calls:
24.0ms
(* z (log (- 1.0 y)))
14.0ms
(* x (log y))
13.0ms
(log (- 1.0 y))

series206.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(* z (log (- 1.0 y)))
53.0ms
(* x (log y))
59.0ms
(log (- 1.0 y))

simplify3.0s

Counts
85 → 85
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0174800
1354763
2781683
31574668
44364664
done5000662

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 1.0) (* z (pow y 2)))
0.3b
(* x (log y))
1.1b
(/ -1/2 (/ (* 1.0 1.0) (* z (pow y 2))))
6.9b
(* z (pow y 2))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
38×add-cbrt-cube
29×add-sqr-sqrt
25×div-exp
24×prod-exp
21×add-cube-cbrt *-un-lft-identity
20×times-frac
13×cbrt-undiv
12×associate-*r*
10×cbrt-unprod
7×pow1
6×log-prod associate-*l* associate-/r* div-inv
5×pow-to-exp pow-exp unswap-sqr
4×expm1-log1p-u unpow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×distribute-rgt-in distribute-lft-in
2×frac-2neg clear-num *-commutative unpow2 sqr-pow
1×pow-prod-down associate-/r/ log-pow
Counts
4 → 133
Calls
4 calls:
33.0ms
(/ (* 1.0 1.0) (* z (pow y 2)))
13.0ms
(* x (log y))
23.0ms
(/ -1/2 (/ (* 1.0 1.0) (* z (pow y 2))))
17.0ms
(* z (pow y 2))

series184.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* 1.0 1.0) (* z (pow y 2)))
58.0ms
(* x (log y))
53.0ms
(/ -1/2 (/ (* 1.0 1.0) (* z (pow y 2))))
42.0ms
(* z (pow y 2))

simplify1.1s

Counts
145 → 145
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02131787
14601655
215231412
done50011407

prune676.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x (log y)) (* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0)))))
0.0b
(* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))))
0.0b
(* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))
0.3b
(* x (log y))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×distribute-rgt-in distribute-lft-in
24×log-prod
22×add-cube-cbrt *-un-lft-identity
18×associate-+r+
16×prod-diff
15×pow1
12×associate--l+
10×add-exp-log associate-*r* add-cbrt-cube
9×associate-*l*
6×associate-+l+ add-log-exp
5×log-pow
4×expm1-log1p-u sub-neg log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*r/ fma-udef
1×+-commutative flip3-- fma-def flip3-+ sum-log flip-- flip-+
Counts
4 → 127
Calls
4 calls:
22.0ms
(+ (* x (log y)) (* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0)))))
33.0ms
(* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))))
11.0ms
(* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))
13.0ms
(* x (log y))

series396.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (* x (log y)) (* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0)))))
112.0ms
(* z (- (log 1.0) (* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))))
105.0ms
(* y (fma (/ 1/2 1.0) (/ y 1.0) 1.0))
59.0ms
(* x (log y))

simplify2.5s

Counts
139 → 139
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02282473
14812331
212022115
344132061
done50002053

prune628.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (cbrt y)) x)
0.3b
(+ (* x (* 2 (log (cbrt y)))) (* (log (cbrt y)) x))
0.6b
(cbrt y)
0.6b
(cbrt y)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
24×distribute-rgt-in associate-+l+ log-prod distribute-lft-in
18×cbrt-prod add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×pow1/3 associate-*r*
2×log-pow
1×+-commutative fma-def flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 86
Calls
4 calls:
21.0ms
(* (log (cbrt y)) x)
31.0ms
(+ (* x (* 2 (log (cbrt y)))) (* (log (cbrt y)) x))
1.0ms
(cbrt y)
1.0ms
(cbrt y)

series778.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (log (cbrt y)) x)
142.0ms
(+ (* x (* 2 (log (cbrt y)))) (* (log (cbrt y)) x))
252.0ms
(cbrt y)
219.0ms
(cbrt y)

simplify2.1s

Counts
98 → 98
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0132968
1321855
21006698
done5000596

prune543.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes226.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02532
13232
done3232

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.2s24209×body80nan
1.1s5516×body80valid
465.0ms900×body640valid
351.0ms446×body1280valid
204.0ms723×body320valid
71.0ms449×body160valid