Details

Time bar (total: 15.4s)

sample182.0ms

Algorithm
intervals
Results
63.0ms1164×body80nan
22.0ms378×body80valid
5.0ms16×body640valid
3.0ms16×body320valid
1.0ms1×body1280valid
1.0ms8×body160valid

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110
done500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* y (- (log z) t))
0.3b
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
1.0b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.8b
(log (- 1.0 z))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
72×prod-diff
69×add-sqr-sqrt
66×*-un-lft-identity
57×add-cube-cbrt
53×distribute-rgt-in distribute-lft-in
38×associate-+r+
34×associate-+l+
28×pow1
27×log-prod
22×associate--l+
20×log-pow
10×associate-*r/ associate-*r*
8×add-exp-log add-cbrt-cube
6×sub-neg flip3-- associate-*l* flip-- add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u frac-add log1p-expm1-u difference-of-squares
2×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative fma-def flip3-+ rem-log-exp exp-sum sum-log flip-+
Counts
4 → 188
Calls
4 calls:
28.0ms
(* y (- (log z) t))
111.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
35.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms
(log (- 1.0 z))

series493.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* y (- (log z) t))
177.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
199.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms
(log (- 1.0 z))

simplify96.0ms

Counts
200 → 200
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09472029
137911591
250011590
done50011590

prune850.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b
(* y (- (log z) t))
0.2b
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
1.0b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
168×prod-diff
156×*-un-lft-identity
144×add-sqr-sqrt
110×add-cube-cbrt
108×distribute-rgt-in distribute-lft-in
92×associate--l+
74×associate-+r+
48×pow1
38×log-pow
34×associate-+l+
31×distribute-lft-out--
24×log-prod
17×associate-*r*
14×difference-of-squares
12×sub-neg associate-*r/
10×add-cbrt-cube
9×add-exp-log associate-*l*
6×flip3-- flip-- add-log-exp
4×expm1-log1p-u frac-add log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative fma-def flip3-+ exp-sum sum-log flip-+
Counts
4 → 306
Calls
4 calls:
691.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
28.0ms
(* y (- (log z) t))
483.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
250.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
71.0ms
(* y (- (log z) t))
247.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
253.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify147.0ms

Counts
318 → 318
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
011196148
146764554
250014552
done50014552

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite753.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
101×*-un-lft-identity
80×times-frac
79×associate-*r*
76×add-cube-cbrt
60×prod-diff
56×unpow-prod-down
40×associate--l+
37×distribute-rgt-in distribute-lft-in
30×add-exp-log
24×unpow2 sqr-pow
23×pow1
19×unswap-sqr
17×distribute-lft-out--
13×log-pow add-cbrt-cube
12×prod-exp
9×div-exp associate-*l*
7×difference-of-squares
6×pow-to-exp log-prod pow-exp
4×expm1-log1p-u sub-neg cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*r/ pow-prod-down *-commutative
2×fma-udef
1×cbrt-undiv flip3-- exp-sum flip-- div-inv
Counts
4 → 243
Calls
4 calls:
36.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
692.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
11.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
104.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
236.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
257.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify116.0ms

Counts
255 → 255
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
010313935
147072803
250012707
done50012707

prune853.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.3b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.3b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.3b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-prod expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
1×pow1/3 exp-sum
Counts
4 → 44
Calls
4 calls:
2.0ms
(cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series1.0s

Counts
4 → 12
Calls
4 calls:
263.0ms
(cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
257.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
248.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
252.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify45.0ms

Counts
56 → 56
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0180929
1420805
21369799
35002778
done5002778

prune424.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
12915
done2915

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.2s40570×body80nan
751.0ms12463×body80valid
129.0ms381×body640valid
80.0ms385×body320valid
50.0ms71×body1280valid
36.0ms281×body160valid