Details

Time bar (total: 5.1s)

sample75.0ms

Algorithm
intervals
Results
24.0ms56×body1280valid
17.0ms314×body80valid
8.0ms33×body640valid
3.0ms21×body320valid
3.0ms59×body80overflowed
1.0ms8×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (38.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
2.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
28×flip3-- flip3-+ flip-- flip-+
18×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u associate-*l* log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 158
Calls
4 calls:
18.0ms
(* (+ 1.0 eps) x)
6.0ms
(exp (- (* (+ 1.0 eps) x)))
9.0ms
(exp (- (* (- 1.0 eps) x)))
45.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (+ 1.0 eps) x)
24.0ms
(exp (- (* (+ 1.0 eps) x)))
30.0ms
(exp (- (* (- 1.0 eps) x)))
180.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify150.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
012913707
147633415
250013397

prune453.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

5.6b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

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 (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series40.0ms

Counts
1 → 3
Calls
1 calls:
40.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify30.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04289
113678
272278
3500275

prune50.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* x eps) (* 1.0 x)))
0.0b
(exp (- (* x eps) (* 1.0 x)))
0.0b
(exp (fma x eps (* 1.0 x)))
2.2b
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
9×exp-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity exp-sum
5×rem-exp-log
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×sub-neg exp-diff diff-log prod-diff fma-udef
Counts
4 → 60
Calls
4 calls:
21.0ms
(exp (- (* x eps) (* 1.0 x)))
17.0ms
(exp (- (* x eps) (* 1.0 x)))
2.0ms
(exp (fma x eps (* 1.0 x)))
0.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

series224.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(exp (- (* x eps) (* 1.0 x)))
17.0ms
(exp (- (* x eps) (* 1.0 x)))
15.0ms
(exp (fma x eps (* 1.0 x)))
174.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

simplify79.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0186644
1502565
22481541
35002531

prune323.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* x eps) (* 1.0 x)))
0.0b
(exp (fma x eps (* 1.0 x)))
0.3b
(log1p (exp (fma x eps (* 1.0 x))))
2.2b
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (expm1 (log1p (exp (fma x eps (* 1.0 x)))))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
6×add-sqr-sqrt add-cube-cbrt exp-prod *-un-lft-identity
5×expm1-log1p-u
4×pow1 add-exp-log exp-sum add-cbrt-cube log1p-expm1-u
3×rem-exp-log
2×fma-udef
1×sub-neg log1p-udef exp-diff diff-log log1p-expm1 prod-diff
Counts
4 → 53
Calls
4 calls:
17.0ms
(exp (- (* x eps) (* 1.0 x)))
2.0ms
(exp (fma x eps (* 1.0 x)))
0.0ms
(log1p (exp (fma x eps (* 1.0 x))))
0.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (expm1 (log1p (exp (fma x eps (* 1.0 x)))))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(exp (- (* x eps) (* 1.0 x)))
14.0ms
(exp (fma x eps (* 1.0 x)))
34.0ms
(log1p (exp (fma x eps (* 1.0 x))))
218.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (expm1 (log1p (exp (fma x eps (* 1.0 x)))))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

simplify84.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0218637
1554551
22569532
35002521

prune293.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

96% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.8b

bsearch166.0ms

Steps
ItersRangePoint
10
9.155891339580972e-07
611368.3395468491
9.62605629459005

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05135
16335
26335

end0.0ms

sample2.2s

Algorithm
intervals
Results
727.0ms1671×body1280valid
542.0ms9986×body80valid
326.0ms1257×body640valid
105.0ms637×body320valid
99.0ms1893×body80overflowed
38.0ms361×body160valid