Details

Time bar (total: 16.5s)

sample102.0ms

Algorithm
intervals
Results
38.0ms809×body80nan
9.0ms183×body80valid
8.0ms13×body1280valid
5.0ms18×body640valid
4.0ms21×body320valid
2.0ms23×body160valid

simplify221.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01213
12212
23712
34712
45512
57212
610312
715112
819112
921412
1023512
1123712
done23712

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (log (- 1.0 y)))
0.3b
(* x (log y))
5.7b
(log (- 1.0 y))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×log-prod
18×*-un-lft-identity
12×add-cube-cbrt
10×pow1
add-exp-log distribute-rgt-in distribute-lft-in associate-*r*
add-cbrt-cube
associate-*l*
expm1-log1p-u log-pow log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
flip3-- rem-log-exp flip--
Counts
3 → 76
Calls
3 calls:
7.0ms
(* z (log (- 1.0 y)))
4.0ms
(* x (log y))
6.0ms
(log (- 1.0 y))

series170.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(* z (log (- 1.0 y)))
49.0ms
(* x (log y))
49.0ms
(log (- 1.0 y))

simplify1.1s

Counts
85 → 85
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0174800
1354763
2836682
32016669
done5001667

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
57×prod-diff
56×*-un-lft-identity
51×add-cube-cbrt
40×distribute-rgt-in distribute-lft-in
34×associate-+r+
24×log-prod
22×pow1
14×log-pow
13×associate--l+
11×add-log-exp
10×associate-*r*
add-exp-log add-cbrt-cube
associate-+l+ associate-*l*
sub-neg
expm1-log1p-u log1p-expm1-u
fma-neg distribute-lft-out--
flip3-- diff-log associate-*r/ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod difference-of-squares unswap-sqr
+-commutative fma-def flip3-+ flip-+
Counts
4 → 170
Calls
4 calls:
24.0ms
(- (+ (* x (log y)) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
9.0ms
(+ (* x (log y)) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
15.0ms
(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms
(* x (log y))

series500.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(- (+ (* x (log y)) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
143.0ms
(+ (* x (log y)) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
112.0ms
(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
42.0ms
(* x (log y))

simplify815.0ms

Counts
182 → 182
Iterations

Useful iterations: done (808.0ms)

IterNodesCost
02966298
15994630
214883922
done50003838

prune657.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
pow1/3
add-exp-log swap-sqr associate-*r* associate-*l*
expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
pow-prod-down pow-sqr pow-prod-up
pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt y) (cbrt y))
0.0ms
(cbrt y)
0.0ms
(cbrt y)
1.0ms
(cbrt y)

series821.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(* (cbrt y) (cbrt y))
198.0ms
(cbrt y)
201.0ms
(cbrt y)
196.0ms
(cbrt y)

simplify4.2s

Counts
93 → 93
Iterations

Useful iterations: 4 (2.2s)

IterNodesCost
065554
1119495
2322423
31163405
43785400
done5000400

prune506.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.2b
(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.3b
(* x (log y))
0.3b
(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
192×sqrt-prod
168×prod-diff
129×add-sqr-sqrt
127×*-un-lft-identity
117×add-cube-cbrt
95×distribute-rgt-in distribute-lft-in
88×associate-+r+
40×pow1
27×log-pow
20×associate-*r*
13×add-exp-log add-cbrt-cube
12×log-prod
10×associate-*r/
associate-*l*
associate-+l+ add-log-exp
flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+
expm1-log1p-u frac-times sub-neg log1p-expm1-u difference-of-squares
flip3-- *-commutative flip-- distribute-lft-out distribute-lft-out--
associate-*l/ unswap-sqr
+-commutative fma-def sum-log
Counts
4 → 285
Calls
4 calls:
21.0ms
(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
24.0ms
(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
4.0ms
(* x (log y))
57.0ms
(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series883.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
201.0ms
(* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
45.0ms
(* x (log y))
497.0ms
(* (* z (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify1.9s

Counts
297 → 297
Iterations

Useful iterations: 2 (941.0ms)

IterNodesCost
041221483
1107815774
2384011648
done500111648

prune897.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes222.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02333
12733
done2733

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s24450×body80nan
287.0ms5594×body80valid
263.0ms891×body640valid
241.0ms412×body1280valid
119.0ms686×body320valid
46.0ms436×body160valid