Details

Time bar (total: 15.8s)

sample180.0ms

Algorithm
intervals
Results
76.0ms1324×body80nan
25.0ms413×body80valid
5.0ms13×body640valid
3.0ms3×body1280valid
2.0ms10×body320valid
1.0ms9×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize16.0ms

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))

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:
15.0ms
(* y (- (log z) t))
55.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
21.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms
(log (- 1.0 z))

series459.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* y (- (log z) t))
156.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
187.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms
(log (- 1.0 z))

simplify105.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09472029
137911591
250011590

prune660.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))
0.2b
(* 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)))

rewrite1.0s

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:
490.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms
(* y (- (log z) t))
317.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
175.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
73.0ms
(* y (- (log z) t))
221.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
246.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify157.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
011196148
146764554
250014552

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
0.7b
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
0.7b
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
0.7b
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-prod
52×*-un-lft-identity
37×add-sqr-sqrt
22×pow1 distribute-lft-out--
18×cbrt-div
15×add-cube-cbrt swap-sqr
11×log-pow
9×flip3-- pow1/3 associate-*r* associate-*l* flip--
7×difference-of-squares
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 119
Calls
4 calls:
191.0ms
(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
23.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
25.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
23.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

series981.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
234.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
237.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
239.0ms
(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

simplify75.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05272977
119672821
250012531

prune865.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

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)))

rewrite607.0ms

Algorithm
rewrite-expression-head
Rules
168×prod-diff
148×associate-+r+
144×*-un-lft-identity
134×add-sqr-sqrt
108×distribute-rgt-in add-cube-cbrt distribute-lft-in
92×associate--l+
68×associate-+l+
42×pow1
36×log-pow
24×log-prod distribute-lft-out--
16×associate-*r/
12×sub-neg difference-of-squares
8×flip3-- sqrt-pow1 frac-add sqrt-prod flip-- add-log-exp
6×exp-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×+-commutative rem-sqrt-square fma-def flip3-+ pow1/2 exp-sum sum-log flip-+
Counts
4 → 290
Calls
4 calls:
126.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
106.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
170.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
177.0ms
(+ (* 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:
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)))))
282.0ms
(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
251.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
245.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify119.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08495980
128214874
250014626

prune1.9s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes158.0ms

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
04642
15342
25342

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.2s41113×body80nan
767.0ms12663×body80valid
125.0ms361×body640valid
85.0ms406×body320valid
56.0ms78×body1280valid
35.0ms258×body160valid