Details

Time bar (total: 13.0s)

sample208.0ms

Algorithm
intervals
Results
94.0ms1275×body80nan
31.0ms390×body80valid
6.0ms14×body640valid
3.0ms11×body320valid
2.0ms2×body1280valid
1.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune3.0ms

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: 1.6b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b
(* y (- (log z) t))
0.5b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.3b
(log (- 1.0 z))

rewrite51.0ms

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:
9.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
8.0ms
(* y (- (log z) t))
20.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms
(log (- 1.0 z))

series431.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
65.0ms
(* y (- (log z) t))
187.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms
(log (- 1.0 z))

simplify97.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
09041913
135011501
250011500

prune543.0ms

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
(* 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))
0.1b
(* 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)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
208×add-sqr-sqrt
188×*-un-lft-identity
168×prod-diff
142×add-cube-cbrt
108×distribute-rgt-in distribute-lft-in
92×associate--l+
81×associate-*r*
80×times-frac
74×associate-+r+
56×unpow-prod-down
48×pow1
38×log-pow
34×associate-+l+
31×add-exp-log distribute-lft-out--
24×log-prod unpow2 sqr-pow
19×unswap-sqr
14×difference-of-squares
13×associate-*r/ add-cbrt-cube
12×sub-neg prod-exp
9×div-exp associate-*l*
6×pow-to-exp flip3-- pow-exp flip-- add-log-exp
4×expm1-log1p-u frac-add cbrt-unprod log1p-expm1-u
3×pow-prod-down *-commutative
1×cbrt-undiv +-commutative fma-def flip3-+ sum-log flip-+ div-inv
Counts
4 → 397
Calls
4 calls:
20.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
22.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms
(* y (- (log z) t))
33.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
105.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
68.0ms
(* y (- (log z) t))
238.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify95.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015216345
150014737

prune1.2s

Filtered
409 candidates to 214 candidates (52.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4081409
Fresh123
Picked101
Done000
Total4103413

Merged error: 0.0b

Counts
413 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(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
(* 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))
0.4b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
100×*-un-lft-identity
80×times-frac
75×add-cube-cbrt associate-*r*
60×prod-diff
56×unpow-prod-down
40×associate--l+
37×distribute-rgt-in distribute-lft-in
29×add-exp-log
24×unpow2 sqr-pow
21×pow1
18×unswap-sqr
17×distribute-lft-out--
13×log-pow
11×prod-exp add-cbrt-cube
9×div-exp
7×difference-of-squares
6×pow-to-exp log-prod associate-*l* pow-exp
5×add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×exp-prod associate-*r/ cbrt-unprod
2×pow-prod-down *-commutative fma-udef
1×cbrt-undiv flip3-- exp-sum flip-- div-inv rem-exp-log
Counts
4 → 236
Calls
4 calls:
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))))
21.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
23.0ms
(* 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)))

series574.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
54.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
102.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
247.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify118.0ms

Algorithm
egg-herbie
Counts
248 → 248
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
09863704
139662671
250022571

prune697.0ms

Filtered
248 candidates to 128 candidates (51.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2471248
Fresh112
Picked011
Done000
Total2483251

Merged error: 0.0b

Counts
251 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
0.4b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.4b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.4b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
7×swap-sqr associate-*r* associate-*l* fma-udef
6×add-exp-log pow1/3
4×expm1-log1p-u exp-sum add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 75
Calls
4 calls:
7.0ms
(* (cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (cbrt (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)))
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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
435.0ms
(* (cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (cbrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
243.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
249.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
241.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify109.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
02502122
17631877
234301703
350021682

prune462.0ms

Filtered
87 candidates to 67 candidates (77.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New86187
Fresh011
Picked101
Done011
Total87390

Merged error: 0b

Counts
90 → 3

regimes176.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
12915

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.9s40629×body80nan
1.0s12587×body80valid
151.0ms357×body640valid
106.0ms402×body320valid
56.0ms69×body1280valid
42.0ms249×body160valid