Details

Time bar (total: 5.8s)

sample98.0ms

Algorithm
intervals
Results
50.0ms148×body1280valid
25.0ms29×body2560valid
11.0ms54×body640valid
2.0ms16×body320valid
1.0ms8×body160valid
0.0ms1×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize9.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (cos (+ x eps)) (cos x))
2.9b
(cos (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series65.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(- (cos (+ x eps)) (cos x))
14.0ms
(cos (+ x eps))

simplify72.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune113.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
3.3b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×prod-diff add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-neg diff-log log1p-expm1-u
3×sub-neg associate--l+ cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 93
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
22.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series286.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
78.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms
(* (sin x) (sin eps))
127.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0381988
11342837
25002822

prune299.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.1b
(fma (sin x) (sin eps) (cos x))
3.3b
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
3.3b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log expm1-log1p-u log-prod log-pow add-cbrt-cube fma-udef log1p-expm1-u
2×exp-sum
1×rem-log-exp rem-exp-log
Counts
4 → 52
Calls
4 calls:
1.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
0.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
52.0ms
(fma (sin x) (sin eps) (cos x))
130.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))
133.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify44.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0137627
1357554
21340554
35002551

prune279.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 18.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.3b
(log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))))
0.4b
(expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
6.9b
(- (log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
7×add-log-exp
6×pow1 add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×expm1-log1p-u
3×fma-neg associate-*r* associate-*l*
2×log1p-udef diff-log
1×sub-neg expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 72
Calls
4 calls:
4.0ms
(* (sin x) (sin eps))
0.0ms
(log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))))
0.0ms
(expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
4.0ms
(- (log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos x))

series440.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin x) (sin eps))
114.0ms
(log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))))
110.0ms
(expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
174.0ms
(- (log1p (expm1 (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos x))

simplify128.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
0297990
1949798
24739774
35001717

prune219.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 18.9b

regimes230.0ms

Accuracy

85.8% (1.4b remaining)

Error of 16.1b against oracle of 14.8b and baseline of 24.5b

bsearch91.0ms

Steps
ItersRangePoint
8
1.7888545263047805e-09
1.4320063078422164e-06
9.257973088560005e-08
7
-6.670553018524384e-09
-5.401657461917285e-11
-6.569641051506792e-09

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03728
13728

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4461×body1280valid
572.0ms663×body2560valid
391.0ms1865×body640valid
103.0ms680×body320valid
24.0ms252×body160valid
4.0ms79×body80valid