Details

Time bar (total: 13.7s)

sample174.0ms

Algorithm
intervals
Results
72.0ms1270×body80nan
23.0ms371×body80valid
4.0ms11×body640valid
4.0ms16×body320valid
3.0ms4×body1280valid
1.0ms6×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.1b
(* y (- (log z) t))
1.3b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.1b
(log (- 1.0 z))

rewrite104.0ms

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:
51.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
15.0ms
(* y (- (log z) t))
23.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms
(log (- 1.0 z))

series443.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
69.0ms
(* y (- (log z) t))
180.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms
(log (- 1.0 z))

simplify102.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
09472029
137901591
250011590

prune640.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))
1.3b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite733.0ms

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:
27.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
492.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms
(* y (- (log z) t))
174.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
99.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
70.0ms
(* y (- (log z) t))
236.0ms
(+ (* 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
409 → 409
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015216345
150014737

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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
(* 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))
0.6b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite538.0ms

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:
6.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
29.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
490.0ms
(* 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)))

series628.0ms

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)))))
51.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
106.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
242.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify121.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
010313866
142562805
250012708

prune828.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))))))
0.6b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.6b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.6b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite11.0ms

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:
8.0ms
(* (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))))))
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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
418.0ms
(* (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))))))
240.0ms
(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)))
238.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify108.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
02502122
17631877
234301703
350021681

prune513.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

regimes153.0ms

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
03432
13432

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.3s40957×body80nan
794.0ms12519×body80valid
123.0ms354×body640valid
90.0ms409×body320valid
57.0ms79×body1280valid
38.0ms276×body160valid