Details

Time bar (total: 12.3s)

sample195.0ms

Algorithm
intervals
Results
80.0ms1405×body80nan
28.0ms395×body80valid
7.0ms18×body640valid
4.0ms5×body1280valid
3.0ms12×body320valid
1.0ms11×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.7b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b
(* y (- (log z) t))
0.5b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0b
(log (- 1.0 z))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
72×prod-diff
66×add-sqr-sqrt
65×*-un-lft-identity
56×add-cube-cbrt
53×distribute-rgt-in distribute-lft-in
38×associate-+r+
34×associate-+l+
27×log-prod
26×pow1
22×associate--l+
20×log-pow
10×associate-*r/
9×add-log-exp
7×add-exp-log
6×sub-neg flip3-- associate-*r* add-cbrt-cube flip--
5×distribute-lft-out--
4×expm1-log1p-u frac-add log1p-expm1-u difference-of-squares
3×exp-prod associate-*l*
2×log-div sum-log rem-exp-log
1×+-commutative fma-def flip3-+ rem-log-exp exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 182
Calls
4 calls:
12.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
8.0ms
(* y (- (log z) t))
17.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms
(log (- 1.0 z))

series451.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms
(* y (- (log z) t))
190.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms
(log (- 1.0 z))

simplify103.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
09041913
135011501
250011500

prune595.0ms

Filtered
194 candidates to 126 candidates (64.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1904194
Fresh000
Picked101
Done000
Total1914195

Merged error: 0.0b

Counts
195 → 4

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

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
168×prod-diff
155×*-un-lft-identity
141×add-sqr-sqrt
109×add-cube-cbrt
108×distribute-rgt-in distribute-lft-in
92×associate--l+
74×associate-+r+
46×pow1
38×log-pow
34×associate-+l+
31×distribute-lft-out--
24×log-prod
14×difference-of-squares
13×associate-*r*
12×sub-neg associate-*r/
9×add-log-exp
8×add-exp-log add-cbrt-cube
6×flip3-- associate-*l* flip--
4×expm1-log1p-u frac-add log1p-expm1-u
3×exp-prod
2×pow-prod-down prod-exp sum-log *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×+-commutative fma-def flip3-+ exp-sum flip-+
Counts
4 → 300
Calls
4 calls:
24.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
19.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
8.0ms
(* y (- (log z) t))
35.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series602.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
173.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
77.0ms
(* y (- (log z) t))
246.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify160.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
010915982
144694426
250014420

prune985.0ms

Filtered
312 candidates to 159 candidates (51.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3102312
Fresh123
Picked101
Done000
Total3124316

Merged error: 0.0b

Counts
316 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
61×add-sqr-sqrt
60×prod-diff
43×add-cube-cbrt
40×associate--l+
37×distribute-rgt-in distribute-lft-in
21×pow1
17×distribute-lft-out--
13×log-pow
11×associate-*r*
8×add-cbrt-cube
7×add-exp-log difference-of-squares
6×log-prod associate-*l*
5×add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×exp-prod fma-udef
2×associate-*r/ exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- rem-exp-log
Counts
4 → 145
Calls
4 calls:
5.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
23.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
2.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
1.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series775.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
111.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
179.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
256.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify88.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05703486
120922505
250032306

prune451.0ms

Filtered
157 candidates to 76 candidates (48.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1543157
Fresh213
Picked101
Done000
Total1574161

Merged error: 0.0b

Counts
161 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.1b
(fma 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 (fma 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 (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity sqrt-pow1 sqrt-prod
6×pow1 exp-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 exp-sum
Counts
4 → 58
Calls
4 calls:
1.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
1.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
2.0ms
(sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
2.0ms
(sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
256.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
250.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
291.0ms
(sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
285.0ms
(sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
01801098
14131006
214351000
35001988

prune432.0ms

Filtered
70 candidates to 62 candidates (88.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New68270
Fresh033
Picked101
Done000
Total69574

Merged error: 0.0b

Counts
74 → 5

regimes328.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03750
13750

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.3s41978×body80nan
999.0ms12641×body80valid
127.0ms367×body640valid
94.0ms420×body320valid
42.0ms61×body1280valid
34.0ms257×body160valid

Profiling

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