Details

Time bar (total: 3.8s)

sample49.0ms

Algorithm
intervals
Results
21.0ms40×body2560valid
8.0ms40×body1280valid
5.0ms40×body640valid
3.0ms30×body320valid
3.0ms89×body80valid
1.0ms17×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b
(- 1.0 (cos x))
12.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
9.0ms
(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify54.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1694239
22689239
35003239

prune113.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.6b
(- 1.0 (cos x))
2.6b
(- 1.0 (cos x))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
156×times-frac
143×*-un-lft-identity
104×sqrt-prod
89×add-cube-cbrt
40×swap-sqr
28×associate-*r* associate-*l*
24×distribute-lft-out--
18×add-exp-log add-cbrt-cube difference-of-squares
11×pow1
9×unswap-sqr
8×associate-/l* add-log-exp
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod
3×flip3-- associate-/r* flip--
2×sub-neg sqrt-div diff-log associate-/l/
1×pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 206
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
43.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

series173.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (sqrt (- 1.0 (cos x))) x)
48.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
17.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify89.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06672403
133402087
250011922

prune416.0ms

Filtered
218 candidates to 123 candidates (56.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.6b
(- 1.0 (cos x))
2.6b
(- 1.0 (cos x))
2.8b
(log (exp (- 1.0 (cos x))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
72×times-frac
61×*-un-lft-identity
48×sqrt-prod
43×add-cube-cbrt
40×associate-*r*
28×associate-*l*
24×log-pow
20×exp-prod
16×add-exp-log add-cbrt-cube
10×pow1
9×distribute-lft-out-- difference-of-squares unswap-sqr
8×add-log-exp
5×log-prod
4×cbrt-undiv div-exp prod-exp cbrt-unprod
3×sub-neg
2×flip3-- diff-log exp-sum flip-- div-inv
1×frac-times log-div exp-diff associate-*r/ rem-log-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 145
Calls
4 calls:
63.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.0ms
(- 1.0 (cos x))
2.0ms
(- 1.0 (cos x))
7.0ms
(log (exp (- 1.0 (cos x))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
18.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))
22.0ms
(log (exp (- 1.0 (cos x))))

simplify62.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06031575
125671213
250011120

prune392.0ms

Filtered
157 candidates to 101 candidates (64.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ 1.0 (cos x))
2.6b
(- 1.0 (cos x))
2.6b
(- (* 1.0 1.0) (* (cos x) (cos x)))
2.8b
(log (exp (- 1.0 (cos x))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt add-log-exp
6×add-cube-cbrt log-pow
5×pow1 log-prod exp-prod
4×add-exp-log add-cbrt-cube
3×sub-neg difference-of-squares
2×flip3-- diff-log exp-sum flip-- distribute-lft-out--
1×+-commutative log-div sqr-cos flip3-+ exp-diff rem-log-exp sum-log flip-+ distribute-lft-out associate--r+
Counts
4 → 60
Calls
4 calls:
3.0ms
(+ 1.0 (cos x))
3.0ms
(- 1.0 (cos x))
3.0ms
(- (* 1.0 1.0) (* (cos x) (cos x)))
8.0ms
(log (exp (- 1.0 (cos x))))

series83.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ 1.0 (cos x))
18.0ms
(- 1.0 (cos x))
32.0ms
(- (* 1.0 1.0) (* (cos x) (cos x)))
23.0ms
(log (exp (- 1.0 (cos x))))

simplify68.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0247350
1813312
22259312
35001312

prune228.0ms

Filtered
72 candidates to 53 candidates (73.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch83.0ms

Steps
ItersRangePoint
10
9.558161037350472e-13
0.8818080259852756
0.034074837610598666
5
-0.041603525395973645
-0.015510049556855336
-0.03305941206486147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06348
16348

end0.0ms

sample1.5s

Algorithm
intervals
Results
716.0ms1582×body2560valid
278.0ms1255×body1280valid
199.0ms1427×body640valid
91.0ms942×body320valid
74.0ms2280×body80valid
41.0ms514×body160valid