Details

Time bar (total: 15.8s)

sample148.0ms

Algorithm
intervals
Results
56.0ms741×body80nan
15.0ms181×body80valid
15.0ms32×body640valid
7.0ms6×body1280valid
5.0ms21×body320valid
3.0ms17×body160valid

simplify4.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01417
12716
25616
310216
424016
556916
6128016
7246416
8324316
9343616
10344016
done344016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.1b
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
5.7b
(log (- 1.0 y))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
16×add-cube-cbrt
15×log-prod
9×prod-diff
8×pow1
7×add-exp-log
6×add-cbrt-cube add-log-exp
5×distribute-rgt-in distribute-lft-in associate-*l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×flip3-- fma-neg flip--
2×log-div associate-*l/ log-pow fma-udef
1×sub-neg diff-log rem-log-exp pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
17.0ms
(* (- z 1.0) (log (- 1.0 y)))
0.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
3.0ms
(log (- 1.0 y))

series346.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
43.0ms
(* (- z 1.0) (log (- 1.0 y)))
115.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
41.0ms
(log (- 1.0 y))

simplify1.7s

Counts
104 → 104
Iterations

Useful iterations: 3 (743.0ms)

IterNodesCost
02141881
14791718
213491519
343051388
done50011388

prune322.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
35×*-un-lft-identity
33×prod-diff
28×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
12×pow1
7×flip3-- associate--l+ log-pow flip--
6×log-prod associate-*r*
5×add-exp-log associate-*l* add-cbrt-cube add-log-exp
4×frac-times distribute-lft-out--
3×expm1-log1p-u sub-neg fma-neg log1p-expm1-u difference-of-squares
2×associate-*r/ associate-*l/ fma-udef
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 106
Calls
3 calls:
3.0ms
(- (fma (- 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)
26.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series367.0ms

Counts
3 → 9
Calls
3 calls:
190.0ms
(- (fma (- 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)
67.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
110.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify612.0ms

Counts
115 → 115
Iterations

Useful iterations: done (607.0ms)

IterNodesCost
02375385
14934186
217983513
done50003408

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (* z (pow y 2)))
0.0b
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
0.1b
(fma (- x 1.0) (log y) (- (* 0.5 (pow y 2)) (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
7.4b
(* z (pow y 2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube
10×prod-exp
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
6×pow1 associate-*l*
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×pow-to-exp pow-exp *-commutative fma-udef unpow2 sqr-pow
1×pow-prod-down
Counts
4 → 70
Calls
4 calls:
8.0ms
(* 0.5 (* z (pow y 2)))
0.0ms
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
0.0ms
(fma (- x 1.0) (log y) (- (* 0.5 (pow y 2)) (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
6.0ms
(* z (pow y 2))

series229.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* 0.5 (* z (pow y 2)))
83.0ms
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
79.0ms
(fma (- x 1.0) (log y) (- (* 0.5 (pow y 2)) (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
32.0ms
(* z (pow y 2))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: 3 (287.0ms)

IterNodesCost
01101038
1229990
2656853
32418803
done5001803

prune280.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.1b
(fma (- x 1.0) (log y) (/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.3b
(* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
22.5b
(/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
16×distribute-rgt-in add-cube-cbrt distribute-lft-in
15×pow1
13×add-exp-log add-cbrt-cube
12×log-prod flip3-- associate--l+ flip--
8×frac-times associate-*l* associate-/l/
7×associate-*r*
5×times-frac associate-/r*
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u distribute-lft-out add-log-exp
3×swap-sqr prod-exp cbrt-unprod fma-udef
2×cbrt-undiv sub-neg div-exp prod-diff pow-prod-down associate-/r/ log-pow *-commutative difference-of-squares unswap-sqr
1×pow2 frac-2neg flip3-+ pow-plus clear-num pow-sqr pow-prod-up flip-+ div-inv associate-/l* distribute-lft-out--
Counts
4 → 125
Calls
4 calls:
3.0ms
(* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.0ms
(fma (- x 1.0) (log y) (/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
24.0ms
(* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
22.0ms
(/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series861.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
315.0ms
(fma (- x 1.0) (log y) (/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
287.0ms
(* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
218.0ms
(/ (* (- z 1.0) (- (* (log 1.0) (log 1.0)) (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify1.1s

Counts
137 → 137
Iterations

Useful iterations: 2 (443.0ms)

IterNodesCost
02636826
16776219
229685297
done50005297

prune586.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes286.0ms

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 (0.0ms)

IterNodesCost
01826
12226
done2226

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s24144×body80nan
330.0ms5858×body80valid
248.0ms784×body640valid
168.0ms268×body1280valid
131.0ms698×body320valid
48.0ms416×body160valid