Details

Time bar (total: 6.1s)

sample108.0ms

Algorithm
intervals
Results
53.0ms131×body1280valid
22.0ms23×body2560valid
19.0ms73×body640valid
4.0ms17×body320valid
1.0ms9×body160valid
0.0ms3×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize15.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (cos (+ x eps)) (cos x))
3.5b
(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))

series67.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify80.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune116.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize18.0ms

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))
3.9b
(- (- (* (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:
3.0ms
(* (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))

series312.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos x) (cos eps))
86.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
51.0ms
(* (sin x) (sin eps))
134.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0381989
11342838
25002822

prune323.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
3.9b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×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
2 → 20
Calls
2 calls:
0.0ms
(fma (sin x) (sin eps) (cos x))
0.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series196.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(fma (sin x) (sin eps) (cos x))
140.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify116.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune149.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (expm1 (* (sin x) (sin eps))))
0.1b
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
0.2b
(* (sin x) (sin eps))
3.9b
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt prod-diff
14×add-log-exp
7×diff-log
6×pow1 add-exp-log add-cbrt-cube
5×associate--l+
4×expm1-log1p-u fma-neg log1p-expm1-u
3×sub-neg log1p-udef associate-*r* associate-*l*
2×flip3-- flip--
1×associate--l- log1p-expm1 pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 87
Calls
4 calls:
0.0ms
(log1p (expm1 (* (sin x) (sin eps))))
4.0ms
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
4.0ms
(* (sin x) (sin eps))
23.0ms
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

series439.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(log1p (expm1 (* (sin x) (sin eps))))
126.0ms
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
45.0ms
(* (sin x) (sin eps))
177.0ms
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03561204
11320889
25001875

prune277.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.2b

regimes195.0ms

Accuracy

87.4% (1.3b remaining)

Error of 16.4b against oracle of 15.1b and baseline of 25.4b

bsearch146.0ms

Steps
ItersRangePoint
9
2.5675937259375084e-20
4.470557786745182e-11
4.3834693427398484e-11
9
-5.033370145566524e-07
-1.9815489217883408e-12
-4.334975105484835e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04440
14840
24840

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s4420×body1280valid
615.0ms660×body2560valid
527.0ms1868×body640valid
135.0ms694×body320valid
44.0ms285×body160valid
6.0ms73×body80valid