Details

Time bar (total: 7.4s)

sample131.0ms

Algorithm
intervals
Results
49.0ms744×body80nan
15.0ms36×body640valid
14.0ms177×body80valid
11.0ms14×body1280valid
7.0ms16×body320valid
2.0ms14×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0227
1386
2536
3616
4786
51106
61756
72846
83636
93926
104766
114766

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.3b
(log (- 1.0 y))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt log-prod *-un-lft-identity
3×pow1 add-exp-log add-cube-cbrt
2×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u add-log-exp
1×flip3-- rem-log-exp log-pow flip-- fma-udef distribute-lft-out-- difference-of-squares
Counts
2 → 28
Calls
2 calls:
0.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
3.0ms
(log (- 1.0 y))

series167.0ms

Counts
2 → 6
Calls
2 calls:
119.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
48.0ms
(log (- 1.0 y))

simplify53.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0215218
1571192
21847190
35002189

prune127.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
40×associate--l+
27×prod-diff
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×distribute-rgt-in distribute-lft-in
8×pow1
6×log-prod log-pow
4×add-log-exp
3×sub-neg
2×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×flip3-- fma-neg diff-log flip-- fma-udef
Counts
2 → 62
Calls
2 calls:
19.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series300.0ms

Counts
2 → 6
Calls
2 calls:
124.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
175.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify146.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
02831362
1896858
24590847
35001846

prune535.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series172.0ms

Counts
1 → 3
Calls
1 calls:
172.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify121.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 4 (117.0ms)

IterNodesCost
083180
1228152
2781152
33746152
45001150

prune85.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.0b
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.1b
(fma (log y) x (+ (* z (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))) (fma (fma (- (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 1 (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- t))))
0.5b
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×flip3-+ swap-sqr flip-+
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod fma-udef
Counts
4 → 103
Calls
4 calls:
3.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
3.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.0ms
(fma (log y) x (+ (* z (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))) (fma (fma (- (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 1 (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- t))))
19.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series636.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
70.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
395.0ms
(fma (log y) x (+ (* z (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))) (fma (fma (- (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 1 (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- t))))
102.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
03411713
114161521
250021460

prune606.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes190.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02212
12212

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.6s24078×body80nan
453.0ms5508×body80valid
380.0ms915×body640valid
313.0ms412×body1280valid
200.0ms744×body320valid
77.0ms452×body160valid