Details

Time bar (total: 5.9s)

sample104.0ms

Algorithm
intervals
Results
26.0ms53×body1280valid
24.0ms56×body10240exit
16.0ms278×body80valid
8.0ms30×body640valid
8.0ms26×body320valid
1.0ms11×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
31×flip3-- flip--
27×flip3-+ flip-+
19×un-div-inv
15×add-sqr-sqrt
12×exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 associate-*l* add-cbrt-cube
5×add-exp-log
4×expm1-log1p-u log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 167
Calls
4 calls:
13.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
20.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
26.0ms
(exp (- (* (+ 1.0 eps) x)))
31.0ms
(exp (- (* (- 1.0 eps) x)))
194.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify141.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
012853925
145753627
250013589

prune472.0ms

Filtered
179 candidates to 100 candidates (55.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- 2.0 (* 1.0 (pow x 2)))
8.0b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef
Counts
2 → 30
Calls
2 calls:
3.0ms
(- 2.0 (* 1.0 (pow x 2)))
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series100.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(- 2.0 (* 1.0 (pow x 2)))
42.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify67.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0126221
1412193
22139191
35001171

prune114.0ms

Filtered
36 candidates to 27 candidates (75.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

8.0b
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
13.5b
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
3.0ms
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

series346.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
280.0ms
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0142554
1441496
22194496
35001492

prune185.0ms

Filtered
45 candidates to 36 candidates (80.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))))
0.0b
(log1p (expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))))
8.0b
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
13.5b
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×pow1 expm1-log1p-u add-log-exp
3×associate-/r* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num fma-udef div-inv expm1-udef
Counts
4 → 61
Calls
4 calls:
1.0ms
(expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))))
1.0ms
(log1p (expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))))
1.0ms
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
3.0ms
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

series417.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))))
147.0ms
(log1p (expm1 (fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))))
68.0ms
(fma (pow x 3) 0.6666666666666667 (/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0)))
143.0ms
(/ (fma 2.0 2.0 (* (- (* 1.0 1.0)) (pow x 4))) (fma (pow x 2) 1.0 2.0))

simplify91.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
0210902
1611798
22713797
35001791

prune297.0ms

Filtered
73 candidates to 59 candidates (80.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

regimes117.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.5b

bsearch144.0ms

Steps
ItersRangePoint
9
0.011591005997014599
42925490.781275615
10.613056418230078

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05755
16655
26755
36755

end0.0ms

sample2.8s

Algorithm
intervals
Results
780.0ms1950×body10240exit
709.0ms1669×body1280valid
537.0ms9991×body80valid
322.0ms1301×body640valid
109.0ms645×body320valid
32.0ms306×body160valid