Details

Time bar (total: 6.3s)

sample113.0ms

Algorithm
intervals
Results
28.0ms62×body10240exit
28.0ms355×body80valid
21.0ms43×body1280valid
12.0ms38×body640valid
4.0ms20×body320valid
2.0ms14×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (* (- 1.0 eps) x))
5.9b
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube
8×add-exp-log
7×add-sqr-sqrt add-cube-cbrt exp-prod
4×pow1 expm1-log1p-u times-frac log1p-expm1-u associate-/l*
3×rem-exp-log
2×cbrt-undiv exp-to-pow div-exp associate-/l/ distribute-lft-out
1×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in frac-2neg flip3-+ exp-diff diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod flip-+ fma-udef div-inv
Counts
4 → 69
Calls
4 calls:
26.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
3.0ms
(exp (* (- 1.0 eps) x))
0.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
26.0ms
(exp (- (* (+ 1.0 eps) x)))
24.0ms
(exp (* (- 1.0 eps) x))
230.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0365706
11230610
25001590

prune295.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
4.0b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.3b
(/ (pow x 3) eps)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
31×add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
13×add-exp-log
12×cube-prod associate-/l*
8×associate-*r*
7×add-cbrt-cube
6×sqr-pow
4×cube-mult unpow3 unswap-sqr
3×pow1 expm1-log1p-u div-exp associate-*l* prod-exp associate-/r* log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp unpow2
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 106
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms
(/ (pow x 3) eps)

series95.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 0.5 (pow x 2))
50.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms
(/ (pow x 3) eps)

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0305506
11561465
25001451

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
4.0b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.3b
(/ (pow x 3) eps)
6.3b
(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/l*
9×add-exp-log
6×add-cbrt-cube
5×expm1-log1p-u
4×pow1 cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×div-exp associate-/r*
1×cbrt-undiv pow-to-exp log1p-udef expm1-log1p frac-2neg log1p-expm1 pow-exp clear-num fma-udef div-inv expm1-udef
Counts
4 → 99
Calls
4 calls:
0.0ms
(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms
(/ (pow x 3) eps)
0.0ms
(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
596.0ms
(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
51.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms
(/ (pow x 3) eps)
152.0ms
(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0294632
11263583
25001582

prune319.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log 2.0) (* 0.25 (pow x 2)))
0.0b
(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 fma-neg prod-diff
3×log-prod associate--l+ log1p-expm1-u add-log-exp
2×add-exp-log expm1-log1p-u log-pow add-cbrt-cube
1×sub-neg expm1-log1p flip3-- diff-log flip-- expm1-udef
Counts
2 → 36
Calls
2 calls:
4.0ms
(- (log 2.0) (* 0.25 (pow x 2)))
0.0ms
(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

series305.0ms

Counts
2 → 6
Calls
2 calls:
249.0ms
(- (log 2.0) (* 0.25 (pow x 2)))
55.0ms
(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

simplify63.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0143278
1448242
21874240
35001216

prune90.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

regimes64.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 17.1b

bsearch154.0ms

Steps
ItersRangePoint
10
5.939545479408298e-16
2001.8961909206312
1.3945538910343576

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04029
14629
24629

end0.0ms

sample3.0s

Algorithm
intervals
Results
874.0ms2035×body10240exit
790.0ms1726×body1280valid
590.0ms10226×body80valid
333.0ms1273×body640valid
110.0ms637×body320valid
34.0ms308×body160valid