Details

Time bar (total: 16.8s)

sample182.0ms

Algorithm
intervals
Results
74.0ms1324×body80nan
27.0ms413×body80valid
5.0ms13×body640valid
3.0ms3×body1280valid
2.0ms10×body320valid
1.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (29.0ms)

IterNodesCost
01718
13018
25818
311118
428217
595517
6465817
done500017

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y (- (log z) t))
0.3b
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.5b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.8b
(log (- 1.0 z))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt log-prod
24×*-un-lft-identity
22×associate--l+
17×distribute-rgt-in distribute-lft-in
15×add-cube-cbrt
14×associate-+r+
10×pow1 associate-+l+ 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×frac-add difference-of-squares
2×log-div pow-prod-down prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ rem-log-exp exp-sum sum-log flip-+
Counts
4 → 107
Calls
4 calls:
13.0ms
(* y (- (log z) t))
52.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
14.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms
(log (- 1.0 z))

series466.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* y (- (log z) t))
161.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
188.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms
(log (- 1.0 z))

simplify690.0ms

Counts
119 → 119
Iterations

Useful iterations: done (686.0ms)

IterNodesCost
02751996
16661916
223371781
done50011780

prune448.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

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))
0.2b
(* y (- (log z) t))
0.3b
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.5b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
44×associate--l+
28×add-sqr-sqrt *-un-lft-identity
24×distribute-rgt-in log-prod distribute-lft-in
18×add-cube-cbrt
17×associate-*r*
14×associate-+r+
12×pow1 sub-neg associate-*r/
10×associate-+l+ add-cbrt-cube
9×add-exp-log associate-*l*
7×distribute-lft-out--
6×flip3-- flip-- add-log-exp
4×frac-add
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×log-pow difference-of-squares
1×+-commutative flip3-+ exp-sum sum-log flip-+
Counts
4 → 129
Calls
4 calls:
434.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
13.0ms
(* y (- (log z) t))
325.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
300.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series639.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
71.0ms
(* y (- (log z) t))
222.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
244.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify751.0ms

Counts
141 → 141
Iterations

Useful iterations: done (746.0ms)

IterNodesCost
02793684
16673563
225083354
done50003353

prune612.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.2b
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.5b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.5b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
44×associate--l+
28×associate-+r+
24×distribute-rgt-in log-prod distribute-lft-in
20×associate-+l+
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity associate-*r/
12×sub-neg
8×flip3-- sqrt-pow1 frac-add sqrt-prod flip-- add-log-exp
6×pow1 exp-prod
4×add-exp-log add-cbrt-cube
2×+-commutative rem-sqrt-square flip3-+ pow1/2 exp-sum sum-log flip-+
Counts
4 → 112
Calls
4 calls:
110.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
109.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
103.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
104.0ms
(+ (* 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:
281.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
281.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
241.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
242.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify488.0ms

Counts
124 → 124
Iterations

Useful iterations: done (483.0ms)

IterNodesCost
01814568
14774360
216214278
done50004126

prune789.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
0.0b
(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
0.2b
(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
6.5b
(* a (pow z 2))

rewrite472.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×add-log-exp
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×add-exp-log exp-prod
8×add-cbrt-cube
6×pow1 associate-*l* sum-log
5×unswap-sqr
4×unpow-prod-down prod-exp rem-exp-log
3×distribute-lft-neg-in exp-neg distribute-rgt-neg-in neg-log
2×neg-sub0 distribute-neg-in exp-diff associate-*r/ exp-sum *-commutative cbrt-unprod unpow2 sqr-pow
1×+-commutative pow-to-exp neg-mul-1 associate-+r+ flip3-+ pow-prod-down pow-exp un-div-inv flip-+
Counts
4 → 86
Calls
4 calls:
14.0ms
(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
105.0ms
(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
343.0ms
(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
6.0ms
(* a (pow z 2))

series236.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
49.0ms
(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
88.0ms
(* x (exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
30.0ms
(* a (pow z 2))

simplify546.0ms

Counts
98 → 98
Iterations

Useful iterations: done (542.0ms)

IterNodesCost
01411684
13361625
211851426
done50001368

prune296.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes165.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02530
13230
done3230

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.3s41113×body80nan
785.0ms12663×body80valid
128.0ms361×body640valid
87.0ms406×body320valid
56.0ms78×body1280valid
36.0ms258×body160valid